Why were businesses operating as trusts at one point, and why did the practice fall out of favor?

Why do businesses like to operate as trusts? Because they earn unusually large (monopoly) profits. Why are trusts out of favor? Because the public resents monopolies.

Early in an industrial cycle, there can be "perfect competition," or something close to it. That is, there are a large number of firms in a given "space," all subject to the laws of supply and demand, and guided by the "invisible hand" to maximize social welfare. At any rate, that is the theory.

The problem comes when there were "mergers and acquisitions." There are different mechanisms nowadays, but in the old days, they were effected through trusts. These trusts were "umbrella" organizations that gathered "several" (former competing) companies under one roof, and divided their efforts so that they would not compete with each other (in e.g. the same territory). Less competition means higher profits for each company (and the trust as a whole), but it also means "price gouging" for the public.

Corporations, (C corps, LLCs) have boards of directors. That's normal. A "trust" occurs when two or more companies, particularly in the same industry have identical or very similar boards (say, seven, eight or nine out of ten) board members in common. Then companies that are technically separate and supposedly "competing" with each other are in actual fact, operating under common control. That leads to monopoly power, or else reasonable fears thereof.

Title Question
Why were businesses operating as trusts at one point, and why did the practice fall out of favor?

The "practice" fell out of favor as you say because laws were passed which outlawed them and created an enforcement arm for the Federal government to find them and prosecute them.

• Sherman Antitrust Act (1890)
• Clayton Antitrust Act (1914) - Clarified and refined SAA
• Federal Trade Commission (1914) - enforcement agency

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Sherman Antitrust Act of 1890

• outlaws all combinations that restrain trade between states or with foreign nations.
  • any agreement to fix prices
  • limit industrial output
  • share markets
  • exclude competition
  • selling products at a loss
• illegal all attempts to monopolize any part of trade or commerce in the United States
• Enforceable by the Department of Justice through litigation in the federal courts
• private parties injured by violations are permitted to sue for triple the amount of damages done them.

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Question 1
We say "anti-trust" because historically trusts were the preferred vehicles for operating monopolies. Why trusts?.... Why did trusts particularly suit the desired non-ownership function? Why not some other legal entity, e.g., corporation or partnership?

A Monopoly is a person or corporation that has total control over a segment of the economy. A trust is a type of Monopoly where a group of persons or corporations work together, rather than compete amongst themselves to exhibit the same power over a sector of the economy. While the United States has had both, Trust are more prevalent because it's easier for would be competitors to coordinate than it is for a single entity to dominate a sector of the economy.

( A Cartel, is like a trust. It's a group which owns enough of the market to set prices. OOEC is a cartel. Cartels can have competitors and their control of the market is less than domination, but they still have the power to artificially inflate prices and thus they are still illegal in the US. )

Monopolies and Trusts Trusts are the organization of several businesses in the same industry and by joining forces, the trust controls production and distribution of a product or service, thereby limiting competition. Monopolies are businesses that have total control over a sector of the economy, including prices.

Question 2 I know part of the answer is that there were regulations (laws) on who could own what. What were the ownership prohibitions exactly?

Trusts don't generally occur due to government interference as your question suggests. It is more common for trusts or monopolies to occur because of the lack of government regulations or enforcement. Having said that there are both government created trusts and government sanctioned trust examples.

• US health insurance industry
  An example of the government legislating trusts would be the US health insurance industry. the McCarran Ferguson Act of 1945 established Health Insurance Trusts by exempting health insurance companies from many federal regulations most notable antitrust laws and legally allowing them to collude on prices. In this case it would be state laws which are the most influential on these trusts because federal laws generally aren't applied. Notable exception would be the Affordable Care Act, which didn't fundamentally change the monopoly/trust based structure of the industry but tried to reform it by introducing regulations to make the industry more responsive to consumers..
  • No Pre-existing conditions
  • Corporate overhead including profits capped at 25% of gross sales
  • introduce common descriptions of policies to make them more easily evaluated.
  • established minimum coverages
  • ..... etc....

A free market allows for those who have some advantage to put those who don't out of business, History demonstrates that when the US market was devoid of antitrust laws or those laws where not enforced; Trusts and Monopolies thrive.

Most historic American trusts (railroad, banking, oil, steel, communications, sports) evolved independent from the government, however; since antitrust legislation was first passed by Congress in the late 1880's (Sherman Antitrust Act of 1890) all subsequent monopolies have benefited from the Government regulating bodies looking the other way. Other American trusts which I looked into as being established by the Government fell short of the mark. In these cases it appears they became monopolies prior to receiving government sanction for their monopolies.

• Major League Baseball
  Unlike American Football, Basketball, or Hockey; American baseball enjoys a monopoly and general shield from U.S. antitrust laws. It goes back to the early 1900's when MLB used their dominance over the sport and players to crush would be competitor Leagues. MLB bared players who were not under contract with MLB teams from signing with a competitor league, telling the players they would not be welcomed back into MLB in future contracts. This practice was upheld in Federal Baseball Club of Baltimore v. National League with the claim MLB operates outside of the antitrust laws. This finding placing MLB outside of US antitrust laws has been upheld several times since including just recently in June 12, 2018.

Will Supreme Court Review Challenges to Baseball Antitrust Exemption?
Baseball’s judicially-created antitrust exemption is now nearly 100 years ago. Federal Baseball Club v. National League, 259 U.S. 200 (1922). Justice Holmes’ opinion has stood the test of time

• AT&T
  A monopoly for much of the 20th century being the only company for telephone service in both the United States and Canada. The relationship with the government sanctioning this monopoly was formalized in 1913 with the Kingsbury Commitment and lasted until the early 1980's when AT&T was broken up and the Telephone industry was deregulated.

• Alcoa
  The largest aluminum producer in the world. It was influential in WWII as the United States went from producing 6% of all combatant aircraft in 1939, to 41% in 1944. Alcoa however also developed it's monopoly independent from government mandate. It was having antitrust issues with the government as early as 1911, broken up by court order in 1945. It has since regained much of it's market share and reconsolidated much of the Aluminum manufacturing industry.

History of Alcoa
Judge Learned Hand ruled that although Alcoa had not intended to create its monopoly, the fact remained that it had a monopoly on the domestic aluminum market in violation of antitrust law and it would be in the nation's best interest to break it up.

World War II aircraft production

Question 3
What ultimately made trusts an inferior vehicle for commercial enterprise? In other words, why don't some (non-monopolistic) firms continue to organize as trusts?

Trusts are not an inferior model for conducting business from the perspective of the Trust. Some of the wealthiest men in American History JP Morgan, Rockefeller, Carnegie, and Cornelius Vanderbilt were all beneficiaries of Trusts or Monopolies. To be the head of a monopoly or trust is to be wealthy, powerful, and politically influential.

What makes them inferior vehicles for commerce is from the perspective of the greater economy. Trusts are anti competitive, produce expensive products, and ultimately stifle innovation. They stifle innovation in their sector of the economy as trusts by definition don't compete for market share but dictate to the market. They stifle innovation across the greater economy as the entire economy is forced to pay large overhead and incur greater expenses due to higher costs from the trust (higher transport costs, steel costs, software costs etc). Stated another way monopolies or trusts inhibit the entire economy by taking power out of the hands of consumers along with the incentive to compete and improve ones production for the trust.

As demonstrated businesses still operate as trusts and monopolies today, this is due to a failure to prosecute, failure to take action when prosecuted and a general change of attitudes over the harmfulness of Monopolies. The argument in favor of Monopolies makes note that when Rockefeller's standard oil was broken up into 34 companies. Rockefeller's 90% ownership in Standard Oil then became 90% ownership in 34 competing companies; and Rockefeller made a lot more money than he did previously. Thus the argument goes that predatory monopolies ultimately harm themselves and thus the market itself can take care of the excesses.

The two current answers cover why anti-trust laws exist, but if my reading of your question is correct, what you actually want to know is why most large companies were Trusts in those days, as opposed to C-Corps or LLCs nowadays.

The main difference between a corporation and a business trust is that the former has an owner and therefor is part of your assets, while the latter has a beneficiary and therefor is not part of your assets.

The wiki article on Standard Oil has the reason why they got used in the first place:

In response to state laws trying to limit the scale of companies, Rockefeller and his associates developed innovative ways of organizing, to effectively manage their fast growing enterprise. On January 2, 1882, they combined their disparate companies, spread across dozens of states, under a single group of trustees. By a secret agreement, the existing 37 stockholders conveyed their shares "in trust" to nine trustees: John and William Rockefeller, Oliver H. Payne, Charles Pratt, Henry Flagler, John D. Archbold, William G. Warden, Jabez Bostwick, and Benjamin Brewster.This organization proved so successful that other giant enterprises adopted this "trust" form.

In 1885, Standard Oil of Ohio moved its headquarters from Cleveland to its permanent headquarters at 26 Broadway in New York City. Concurrently, the trustees of Standard Oil of Ohio chartered the Standard Oil Co. of New Jersey (SOCNJ) to take advantages of New Jersey's more lenient corporate stock ownership laws.

(Presumably using trusts was no longer needed when state laws became friendlier with large corporations.)

The wiki article on business trusts has a few lines on why they were phased out:

Although such "corporate trusts" were initially set up to improve the organization of large businesses, they soon faced widespread accusations of abusing their market power to engage in anticompetitive business practices. This caused the term "trust" to become strongly associated with such practices among the American public and led to the enactment in 1890 of the Sherman Antitrust Act, the first U.S. federal competition statute.

Meanwhile, "trust agreements", the legal instruments used to create the corporate trusts, received a hostile reception in state courts during the 1880s and were quickly phased out in the 1890s in favor of other clever devices like holding companies for maintaining corporate control. For example, the Standard Oil Trust terminated its own trust agreement in March 1892. Regardless, the name stuck, and American competition laws are known today as antitrust laws (or anti-trust laws) as a result of the historical public aversion to trusts, while other countries use the term "competition laws" instead.

I'm not privy with the court details that made them go out of favor in the 1880s. The wiki article cites Barak Orbach and Grace E. Campbell Rebling, "The Antitrust Curse of Bigness", 85 S. Cal. L. Rev. 605 (2012)." for that claim.