Wheat and rice are food that humans eat but humans also eat chicken, pork, beef, turkey, eggs, cheese, milk and many other animal products. So what do you think animals in cages and feedlots eat? Corn and more corn. Animals like cattle eat the whole corn plant. Also, the yield of corn plants is much higher and has more nutrients than wheat and rice.

Summary: It's not.

First of all, there is one fatal flaw in the basic assumptions here. Maize is just not the most important crop. It is as of 2016 the biggest grain producer, starch plant and indeed very important. But it is dwarfed by another crop, which is produced at nearly double the weight harvested and used. Rice is eaten by people, maize is eaten mainly by animals. Maize has a few advantages going for it but also a lot of disadvantages. And despite from the correct but too simple: "maize makes more money", it has to be taken into account since when does maize play the role it does.

World wide production for crops in million tons

• Sugar beet: 277.23
• Wheat: 720
• Rice: 741.0
• Maize: 1037.8
• Sugarcane: 1890.7

People and animals may eat maize as is. In the other case of cane it's almost exclusively for highly processes 'food' like sweets? Just in case anyone should ask for causes of the diabetes epidemic ever again. To be fair, the system is by now unfair enough to put varying percentages of all of the above crops into aggro-fuel. (The double g is no typo.)

Just looking at how did maize do as well as it did, compared to wheat and rice, this has to be split up into different classes of factors:

Plant inherent factors

Rice and wheat are C3 carbon fixing plants:

High crop yields are pretty important—for keeping people fed, and also for keeping economies running. If you heard there was a single factor that reduced the yield of wheat by 20% and the yield of soybeans by 36% in the United States, for instance, you might be curious to know what it was.
As it turns out, the factor behind those (real-life) numbers is photorespiration. This wasteful metabolic pathway begins when rubisco, the carbon-fixing enzyme of the Calvin cycle, grabs O₂ rather than CO₂.
It uses up fixed carbon, wastes energy, and tends to happen when plants close their stomata (leaf pores) to reduce water loss. High temperatures make it even worse.
Some plants, unlike wheat and soybean, can escape the worst effects of photorespiration. The C4 and CAM pathways are two adaptations—beneficial features arising by natural selection—that allow certain species to minimize photorespiration. These pathways work by ensuring that Rubisco always encounters high concentrations of CO₂ , making it unlikely to bind to O₂ (C3, C4, and CAM plants)​

Maize is C4. Maize is also quite easy to breed into new varieties, even without genetic engineering. A fact demonstrated by how closely looking wild wheat species are, compared to really puny teosinte from which the native Americans managed to breed maize.

Geographical factors

(WP: List of domesticated plants)

As we know, Eurasia can be seen as oriented East-West, while the Americas can be described as North-South. As soon as a plant is deemed good enough to be cultivated, it spreads geographically. Leaving its natural habitat, those plants need to be bred to adaption. In Eurasia that means mostly for wheat to spread more 'horizontally' on the map than 'vertically'.

Origin and spread of rice

_{Fabio Silva et al.: "Modelling the Geographical Origin of Rice Cultivation in Asia Using the Rice Archaeological Database", PLoS ONE 10(9): e0137024. doi:10.1371/journal.pone.0137024}

Current distribution:

Origin and spread of wheat

Spread into Europe:

(src WP)

As can be seen, wheat was also brought into much higher latitudes early on. That alone cannot fully explain the current distribution between wheat and maize.

Current Wheat cultivation:

Origin and spread of maize

_{(Claudia A. Bedoya: "Genetic diversity and population structure of native maize populations in Latin America and the Caribbean", 2017. DOI)}

Current distribution:

Farming factors

Wheat and maize can only be cultivated on dry land. Rice can also be grown on wet fields. Wheat is good for mechanical harvesting, maize is excellent, rice problematic, depending on method.

Historical coincidences

In Europe, white potatoes and maize caught on more slowly, but the effect was remarkably similar. Old World wheat gave back only 5 grains for every 1 planted, whereas maize returned 25 to 100 (a single ear of modern maize yields about 1,000 grains) and, by the middle of the seventeenth century, had become a staple of the peasants of northern Spain, Italy, and to a lesser extent, southern France. From there maize moved into much of the rest of Europe, and by the end of the eighteenth century, such cornmeal mushes (polenta in Italy) had spread via the Ottoman Empire into the Balkans and southern Russia.
From there, the plant spread toward the Ural Mountains, where rye had long been the only staple that would ripen during the short, often rainy summers. Potatoes not only did well under such conditions, they provided some four times as many calories per acre as rye and, by the first decades of the nineteenth century, were a crucial dietary element in the survival of large numbers of northern Europeans, just as maize had become indispensable to humans in some of the more southerly regions. (Kiple, p3)

Why is this headed coincidence?

Not only was the Columbian exchange necessary. As one of the reasons for slow adoption of maize was found that simply switching a wheat based diet to maize produced in the old world a very vitamin deficient outcome:

[By] the time of Columbus, maize had already become the staff of life in the New World. It was distributed throughout both hemispheres from Argentina and Chile northward to Canada and from sea level to high in the Andes, from swampland to arid conditions and from short to long day lengths. In becoming so widespread, it evolved hundreds of races, each with special adaptations for the environment including special utilities for man.
As maize took root in Europe and Africa as well as in the U.S. South, its new consumers failed to treat it with lime before eating – as the Native Americans, presumably through long experience, had learned to do. The result of maize in inexperienced hands, especially when there was little in the diet to supplement it, was niacin deficiency and the four Ds of pellagra: dermatitis, diarrhea, dementia, and death.
maize is deficient in a number of important nutrients. Zein – the protein in maize – is deficient in lysine, isoleucine, and tryptophan (FAO 1970), and if maize consumers do not supplement their diets with foods containing these amino acids, such as beans, significant growth retardation is an outcome. Moreover, maize, although not deficient in niacin (vitamin B3), contains it in a chemically bound form that, untreated, will withhold the vitamin from the consumer. Consequently, human populations consuming untreated maize frequently develop pellagra, a deficiency disease characterized by a number of symptoms, including rough and irritated skin, mental symptoms, and diarrhea (Roe 1973).

"Market incentives"

As can be seen from the maps above, all three crops can be grown almost around the world. But not ever climate, soil or other conditions make these crop really suited for all regions, even when selecting the most adapted cultivar. One problem yet not discussed is that rice is mostly eaten as is. Wheat is made into flakes, bread and pasta. Wheat is also fed to animals. But maize is eaten by humans, fed to livestock, made into aggro-fuel and turned into maize-oil and corn-syrup as well. Despite being really bad for bread making, maize is indeed more versatile in application.

_{The story of wheat. Ears of plenty. The story of man's staple food. Economist 2005}

But that is only one way to look at it.

More of the earth’s surface is covered by wheat than by any other food crop. Wheat production is the third largest cereal production in the world, after maize and rice. In terms of dietary intake, however, wheat comes second to rice as a main food crop, given the more extensive use of maize as animal feed. Wheat is a hardy crop that can grow in a wide range of environmental conditions and that permits large-scale cultivation and long-term storage, making it key to the emergence of urban societies for millennia. Currently, about 65 percent of the wheat crop is used for food, 17 percent for animal feed, and 12 percent in industrial applications, including biofuels. (Feeding the World) Statistical Yearbook of the Food And Agricultural Organization FAO (PDF)

Even if grown in places where wheat would be a much better choice, suited to the conditions, maize can give a much greater yield, if 'properly' taken care for. In terms of ecology or organic farming this 'proper care' is of course quite disastrous. Large fields of maize monoculture need insane amounts of fertilizer, herbicides and pesticides; and it still depletes the soil on its own, not to mention the mechanised farming effects and erosion. While most of these factors were historically unavailable, and will be unavailable again, due to their unsustainability, they are the most important reason for the unprecedented expansion of maize cultivation.

_{Bob Nielsen: "Historical Corn Grain Yields for the U.S.", 2017.}

This is historically a relatively recent trend, but it continues:

Despite the limitations, we believe that this dataset offers a tremendous opportunity for investigating the impacts of climate variability and change on yields and the influences of agriculture on climate, carbon and nitrogen cycles, water resources, land-use changes and biodiversity, as well as testing the reliability of crop simulations at the global scale.
Analyses of our dataset showed that crop yields became higher and more stable at the global level and the global yields of the three cereal crops (maize, rice and wheat) never stagnated between 1994 and 2006. However, a different picture emerged at the latitudinal-mean level. Our results corroborate the yield stagnation and collapses in some regions that were previously reported and revealed that regions in the low and mid latitudes of the Southern Hemisphere, where many developing countries are located, faced increased year-to-year yield variation in the recent period. Because these regions achieved limited increases in mean yields in the recent period, the increases in year-to-year yield variation were likely to be responsible, at least in part, for the yield stagnation and collapses. Further research is needed to elucidate the mechanisms underlying the linkages between the increased year-to-year yield variation and yield stagnation or collapse.
_{Toshichika Iizumi et al.: "Historical changes in global yields: major cereal and legume crops from 1982 to 2006", Global Ecology and Biogeography, (Global Ecol. Biogeogr.) (2014) 23, 346–357. (PDF)}

Global source for this answer: Kenneth F. Kiple & Kriemhild Coneè Ornelas: "The Cambridge World History of Food", Cambridge University Press, 2000.

The global trend 1961–2016, in tonnes harvested, data source FAO stat, two views, compared to global harvest of 186 most important crops in 1961 and 2016:

So the outright explosive growth of maize and its dominating role compared to other food grains came very recently. It was already well adapted to large climatic regions, is inhrently efficient in using CO₂, is easy to breed, very suitable for industrial agriculture, mechanised harvesting, fertilizer, pesticides and herbicides became available and cheap and the market demanded ever increasing quantities for a wide range of applications, not the least fattening livestock, people and cars. Add to that government subsidies in many countries that further distort the picture. Some really want their farmers to plant so much maize that reliance on ideal market factors seem to be insufficient, and therefore this also negates many of the inherent qualities of the plant itself.

Corn was the top crop for subsidy payments prior to 2011. The Energy Policy Act of 2005 mandated that billions of gallons of ethanol be blended into vehicle fuel each year, guaranteeing demand, but US corn ethanol subsidies were between $5.5 billion and $7.3 billion per year. Producers also benefited from a federal subsidy of 51 cents per gallon, additional state subsidies, and federal crop subsidies that had brought the total to 85 cents per gallon or more. However, the federal ethanol subsidy expired December 31, 2011. (US corn-ethanol producers were shielded from competition from cheaper Brazilian sugarcane-ethanol by a 54-cent-per-gallon tariff; however, that tariff also expired December 31, 2011.)
_{WP: Agricultural subsidy}

Without capitalism, government intervention, industrial agriculture, maize would be much less important. But it's always trumped by other crops. Now it's sugarcane.

Corn is the most versatile of crops.

Rice needs a nearly tropical climate in which to grow, and also lots of water for paddies. These conditions are present mostly in Southeast Asia.

Wheat is a northern crop that does better in dry land. It grows best in Kansas, and areas to the north, and areas to the west of that state.

Corn can be grown in "subtropical" areas such as parts of Mexico, but without needing as much water as rice, and grows well fairly far north, up to parts of Nebraska and basically the Great Lakes region as long as there is enough water (more than is needed for wheat). Thus, it is the crop that is most representative of "growing" climates.