My specialty runs more in the development of football in Europe, but I have a fair amount of crossover in American sport history, in particular baseball so I will concentrate mainly on that.

The short answer for why baseball is what it is today in terms of organization is business interests.

The long answer... baseball has a long and winding history in Americana due to it's simplicity of being reduced to, at it's base, "simply...throwing, hitting, and catching a small ball.” The fact that the game at its most primitive was easily understood to both player and spectator contributed heavily towards its popularity with the American public. The other fact was that it was not segregated off from the classes - in fact it was a game for the lower classes.

The rapid rise in industrialization is where you first start seeing a shift from a game of varying rules to something gaining structure. 1845 marked the founding of the New York Knickerbockers and with them their rules on playing the game, which were for the first time published and codified to be the standard set under which the team played. By the time the civil war rolled around, most teams on the Atlantic coast had adopted the so-called "New York Game."

Now, most of these teams were either barnstorming teams or local teams that existed to play each other. Who was "each other?" Well, everyone likes a home team and employers saw massive value in sponsoring teams for their workers, and the added commercial benefits if their team were 'winners.' This is where business first starts to step in and shape the history of the sport. Up until this point, the game was played strictly by amateurs or people employed by the businesses that sponsored the team. Now, the teams pushed the rules of "amateurism" to the limit, often employing people at close to "no-show" jobs simply to make them available to play on the teams. 1869 marked the occasion when any pretense was lost with the founding of the Cincinnati Red Stockings - an all professional team.

With the founding of all professional clubs came the need for serious organizing, as any all professional club found itself quickly swimming in debt. Major financiers were scarred off by the class of people that enjoyed the game. Most of the teams ended up being supported by gamblers with their own interests in the shape of the game. Kirsch noted in his essay on the history of the game that it wasn't atypical for after a lose for the team to face seriously backlash, "“A large crowd pursued them, and pelted their omnibus with stones as they drove off. Most newspapers blamed the disorders and interference on gambling.”

For the game to succeed (i.e. make money for its investors), it would have to be cleaned up. The problem was that all these teams were independent operations owned outside of a system. The first leagues couldn't address that as they were just confederations of independent enterprises. If you didn't like the rules of one league, you could just join another. So what to do? Enter William A. Hulbert, who established what is recognized as the first true "major" league in 1876, the National League of Professional Base Ball Clubs. The difference here is that Hulbert ruled his league with an iron fist and all details of the league went through him. Players salaries, rules, ticket prices, team locations Hulbert ran it all. Promises and connections were made with local politicians to ensure that Hulbert's teams were the only professionals in town. Then in 1880 the first major distinction was made: players were employees, not professionals. Thus they were not free to jump from team to team as independent contractors, they were bound to a team and most importantly the league/team had full control over players salaries. If a player did not like how much money he was making, he simply couldn't jump to another team to make more. This distinction would not be overturned in full until the late 1970s. Even the creation of the American Association of Base Ball Clubs in 1881 over Hulbert's dictatorial policies failed to fix anything for the players as the two leagues quickly colluded to agree to salary caps and respecting 'reserved' players.

This is how the game finally got towards making money - it cut down on players salaries, enforced rules spread throughout the country, and guaranteed the nobody would compete with them. You were free to remain in the league as long as you could pay for a team - and if you couldn't make the agreed upon amount of games you were thrown out and all your players were no longer under reserve. Because you weren't in the "major leagues" you very quickly wouldn't be making money anymore. There was no need for promotion or relegation as it was all business. If you made money you could be admitted, and if you lost money then goodbye. As the teams were being run from the start as a profit making business owners had little want to see themselves be shuttled down to a lower league.

As for the players, they tried multiple times to form their own leagues but by the end of the 1800s the National League was the only league left mainly because they were the only league that could promise money, respectability, and (most importantly) connections with local politicians. If you wanted to make money, you had to do it within the system.

I didn't touch on the area of the draft as that comes after my area of concentration, but it can be seen as an outgrowth of controlling the allocation of players seen earlier. Before the draft player could sign with whomever offered them the most money. The owners saw this as a potential for spiraling players salaries, so the easiest way to fix this was by allocation (It notably was not popular when implemented in the 1930s and 1940s, with the owner of the New York Yankees calling it, "communism"). As the teams could only exist where the league wanted them, you couldn't rely simply on a hometown pool of athletes.

Sources:

• Davies, Richard O. Sports in American Life: A History
• Riess, Steven A. Major Problems in American Sport History: Documents and Essays