I have leaned quite heavily on a few excerpts about the minors from Bill James' first Historical Baseball Abstract, which is one of the greatest books ever written on the topic, in my opinion.
The minor leagues grew and prospered alongside the majors after the signing of the National Agreement in 1903. No longer were they subject to roster raiding, although, of course, the sale of top players was an important source of revenue.
Some leagues held out joining the new NA, fearing it was just another attempt at establishing yet another major league, but that fear quickly passed, and the minors expanded rapidly. In 1912, the AA classification was added at the top of the system to reflect that expansion. World War I and the brief but intense growth of the Federal League presented a huge challenge to the minors, and by the end of WWI they had contracted down to only 9 leagues.
By the 1920s, however, as the rest of America prospered, so too did the minor leagues. The minor league teams (and remember, this was more a term used by sportswriters in major league cities) viewed themselves and their leagues as independent. There were no formal agreements for player acquisition between the majors and minors. This was the era of minor league dynasties in then-minor league cities like Baltimore, St Paul, Fort Worth, and San Francisco. 15 of milb.com's top 100 minor league teams played in this era. By the end of the decade, the number of teams and leagues had doubled. Modern fans might wonder how these teams were able to succeed year after year in the face of the pressure to sell their top players to major league clubs. According to Bill James, when people ask why minor league superstars like Ox Eckhardt (who logged a career batting average of .367) "didn't get a chance" to play in the majors:
"He's not a player who might have done things if he'd had the chance; he's a player who did things. He played baseball. He made a good living playing baseball. His picture was on baseball cards; he was a local celebrity....if he hit .370 one year, the reason that he wanted to hit .380 the next year was not so he would get called up to a higher level, but so he would get a better contract, just as if he were a 'major leaguer' so his team might win the pennant."
The truth is, that while the major leagues were growing in popularity across the country, player salaries did not keep pace, and the players increasingly rebelled at the tight-fisted treatment they received from the owners, which reached its peak with the Black Sox scandal of 1919. Many minor league players were happier playing there; some had been to the majors, but the majority felt that they were treated better (and in some cases, paid better) in the minors.
At the same time as the minors were flourishing, major league teams were becoming frustrated with the process of procuring talent from those leagues. The legendary Branch Rickey, then GM of the St Louis Cardinals, was growing tired of scouting a player, only to lose him to wealthier teams. With the help of owner Sam Breedon's deep pockets, Rickey began buying interests in teams (often several in the same league) across the minors, making it easier for him to acquire a player when the time was right. Rickey coined the term "farm club," when he compared developing players on minor league teams to "growing players down on the farm like corn." At one point in the 1930s, the Cards had as many as 30 farm teams (modern day teams have 5 or 6). With this elaborate system of amassing talent in place, St Louis won 6 World Series titles between 1926 and 1946.
With the stock market crash of 1929, and the Great Depression which followed, like most American businesses, the minors experienced considerable financial pressures, and their independence on major league baseball to help keep afloat increased.