What's the rationale for shipping coins back to Spain from its colonies?

Too long for a comment, but a few points apparently missed from all the other answers from Wikipedia on Gold Extraction:

Gold occurs principally as a native metal, usually alloyed to a greater or lesser extent with silver (as electrum), or sometimes with mercury (as an amalgam). Native gold can occur as sizeable nuggets, as fine grains or flakes in alluvial deposits, or as grains or microscopic particles (known as color) embedded in rock minerals.

In consequence, most New World gold mining would have been placer mining:

the mining of stream bed (alluvial) deposits for minerals. This may be done by open-pit (also called open-cast mining) or by various surface excavating equipment or tunnelling equipment.

Some of the techniques for (19th century) hydraulic-mining of surface gold are well depicted in the movie Pale Rider, though techniques available before steam engines would have been slower and more crude, with only gravity available as a sufficient energy source

Note that the vast majority of gold occurs as either native metal (ie nuggets) or alloyed with other precious metals; and the minting process then requires very little, and often close to zero, actual refinement.

As a final melt was necessary in any case, to produce objects more easily handled than miscellaneous-sized nuggets (remember, gold is heavy) the choice of pouring into ingot-moulds or coin moulds is really rather arbitrary. Transporting the nuggets as is is a false choice, quite impractical.

The processes by which lower-grade ores could be smelted for their gold weren't developed until 1783 (solubility in a cyanide-water solution) and 1887 (MacArthur-Forrest Process capable of achieving 96% purity from ore). Prior to that time the principle techniques for pre-smelting and smelting basically mimicked the natural production of placer gold, producing odd sizes of gold nuggets.

Ores in which gold occurs in chemical composition with other elements are comparatively rare. They include calaverite, sylvanite, nagyagite, petzite and krennerite.

1. History of Gold Refining
2. The Gold Smelting Process

On another note, a lot of the Silver mined in Spanish Colonies actually never was sent to Spain, a lot of the treasure fleets directly sailed for the Philippines for a period, because Spain used a lot of the silver to trade with China anyway.

John Gareth Darwin talked about this in After Tamerlane, called the Manilla Galleons for the harbour they used, sailed for ~250 years from Manila to America between 1565 & 1815.

Another reason for local coinage, in addition to the excellent points above, is that the Viceroyalties were large economies on their own. The Mexican mint was founded in 1535, before the colony's silver mining sector was developed. The imperial bureaucracy depended upon a standardized means of exchange.

Even though Mexico suffered a lack of monetary liquidity for centuries, it would have been even worse off without that mint. Spain was not too interested in exporting specie to its colonies.

Gold and Silver are worth so much that their "bulk" is very rarely a problem.

Coins make it easier to count them. Their bulk is increased slightly; say by a factor of 2.

This makes gold 10 g/cm^3 and silver 5 g/cm^3.

Now, a ship's hold has to be significantly under 1 g/cm^3 in order for the ship to float (otherwise the interior of a ship is heavier than water; that won't do). For both gold and silver coins, the space that they take up is essentially zero; doubling their density (by having gold or silver blocks) wouldn't improve your cargo handling characteristics.

If the hold must be at 0.5 g/cm^3. Solid gold then would take up at most 2.5% of the hold. If we allocate 2% of the hold to solid gold, the remaining material must have a density of no more than 0.102 g/cm^3. If we allocate 4% of the hold to gold coins, the remaining density of the hold must be no more than 0.104 g/cm^3 and have the same weight: there is no noticable difference.

This holds similarly for silver vs silver coins; both gold and silver and coins are so dense that they take up no noticable volume on an ocean going ship.

Minted coins are easier to count and they have a "trademark" that signifies their quality. The limit on carrying them is going to be weight.

You have to refine your gold/silver anyhow (you aren't going to ship ore), and using coin molds isn't much harder than some kind of solid block.

As an aside, one of the most dangerous thing to ship on the Mississippi back when it was the highway of the USA was pig iron. It is dense (8 g/cm^3) and if it shifted it could knock a hole in the bottom of the boat or cause the ship to tip and sink.

Reducing the density of the metal to coins may be a good thing and make it easier to ship.

Many of the coins shipped to Europe were quickly and crudely minted. These were called cobs. According to a page at Notre Dame University,

The intention in minting these crude but accurately weighed cobs was to produce an easily portable product that could be sent to Spain. In Spain the cobs would be melted down to produce silver jewelry, coins, bars and other items. Cobs also circulated as coinage, many cobs made their way to the English colonies where they were used both as coins in commerce and hoarded as specie.

My interpretation of that passage as it relates to your question is that coins were easier to disburse upon reaching their destination. Bars would have to be melted or cut into accurately weighted pieces, and the traders who transported them may not have had the expertise to do this.

I'm hoping that this answer will resonate with your "theory of colonial economy", although it is not based on historical sources.

Coins shouldn't be viewed as end products manufactured from a raw material. The metal is minted primarily to provide a standard way to quantize and control the content (amount) of the precious metal during circulation. For that reason it is often practical to place a mint close to a mine and manage the two as a secure unit. The coin form essentially promises that the inside is the same metal as the outside and that no part of the treasure was stolen or replaced on the way.

Therefore, knowing how much value was being transferred to Europe might have been practical enough for the transport itself.

Even if the "raw material" is shipped - that is, gold or silver, as distinct from various ores, it is practical to employ standardized precious metal content, standardized weight, standardized shapes. In the end a bar of gold is just a bigger coin.

Ores are too bulky to be transported for long distances. Extraction of the metal reduces weight enough for making it efficient to do so before carrying the material overseas.

Assorted "Golden items" from pre-colonial items were rarely made of gold, but more typically using metallurgic techniques that give you gold on the outside, copper in the inside. Such "manufacture" does not count in our context.

Therefore I'm not surprised that coins were frequently included as a method of getting some silver home.