Because of Baseball and the National League. This post is essentially going to point out a why of the North American exception and leave the why of the Football formation mostly to others.
The National League was created by William Hulbert and Al Spalding (where the Glove’s name comes from) in 1876…but lets back up a second: Professionalization of sports:
The NABBP (first organization governing baseball, started in 1857. Didn’t officially allow professionals until…) 1869: Harry Wright Cincinnati Red Stocking first fully professional team (went 65-0 in the first season, won 84 straight games, lost one in extra innings and as a result encountered massive financial difficulty leading the team to fall apart. That’s getting into a tangent though so I’ll drop it).
the National Association was formed in 1871 as the first professional sports league.
The league had problems: the only requirement was essentially a small ($10) fee for inclusion and this lead to the explosion of teams many of fairly low quality which would fold midway through the season or exploit unbalanced disorganized schedules to the detriment of the league in general (and/or western clubs like Chicago). As Hulbert put it in an anonymous 1875 Chicago Tribune article
The Brooklyn Atlantics are a sample of too many professional clubs; they had never any organization, any association, any backing, or any elements of permanency or responsibility of any kind; they were simply a gang of amateurs and rejected professionals, who played such clubs as they could get to come to them, and shared the proceeds. They were not even a mob, for a mob must have a head…. No one supposes that they ever intended to play any western games; they simply entered the ring to force clubs to play as many games as possible with them, they taking two-thirds of the receipts as on home ground…. First-class visiting clubs under heavy expense have lost money every time they played with them, while the two-thirds which went to the gang was reason enough to get on as many games as they could.^^pulled-from-hulbert's-sabr-bio
Similarly, control over players was a huge concern (I’ve seen both pro player and pro Owner slants to this issue): Owners were worried about either players hopping team before their full contract was finished and the impact of that sort of competition on player wages. Beyond the bottom line concerns this lead to wide swings in inta year team quality if one team was “raided” by another for talent. Hulbert was able to fix these concerns with his creation of an 8 team “national league” in 1876 from among the National Association’s teams. Hulbert’s new league had 5 fundamental aspects
Reserve clause for top 5 players on the team. The reserve clause prevented movement for players tagged with it and by the 1880s it would be expanded to the whole team and lasts until modern free agency destroys it.
territoriality: teams had an exclusive right to play National League baseball within a certain geographical distance of their home base.
higher standards for inclusion into the league (both in cost to participate and size of city considered acceptable for a team)
enforced regular schedule (perhaps it’s not ultimately a special aspect of the national league but it’s important to highlight the importance of these basic financial questions).
Owner predominance.
And that’s how North American sports were born. While the national league had rivals it dealt with (including the last and most successful one: the current American League) sports were built on top of its structure. This is fundamentally incompatible with a European relegation system: the closed restrictive sale of the ability to be a part of the national league was created in part to not have to worry about the nicknames of podunk going under or drawing poorly and thus hurting every other team in the league who had to play them. Similarly the exclusive territorial zone is a huge economic advantage important to National League’s economic success which is incompatible with free relegation or promotion.
American sports leagues followed in the successful path of the National League (when you see multiple teams in the same city that’s always or nearly always the result of pre-established teams from multiple leagues merging into the one surviving professional league).
Brief FA interlude: The story of the Football Association’s early days is pretty simple: there was no hard split from amateur organizations to professional. Instead (like in the US) there were amateur clubs->a pan amateur organization emerged (in the US’ case this was the NABBP)-> the creation of the “English football league” as the top English soccer league (this is not actually the premier league. The EPL emerges in 1992 and that’s not really relevant). Essentially the EFL never breaks from the FA (though there are threats as the FA drags its feet on recognizing professionalism) which is a significant ongoing difference between the two systems. I don’t have the knowledge base to answer questions about the foundation of the EFL.