The idea of minor league teams needing to have major league-sized stadiums is obviously financially pretty much impossible in major American sports such as baseball. See, we think that all of the teams in each league should all theoretically actually have a chance, instead of having some super-good teams and then some that are effectively AAA teams in the "major league" but with no chance to actually win before they get dumped down to the next tier again... that's a quite unfair system. The American system of a pro team with attached minor league teams is a better one.
And the playoffs don't take a whole year like the Champion's League, either! The longest playoffs (basketball and hockey) take a few months, but nothing more than that. Instead of the European system of uneven national leagues below with the Champion's League for winners, in most US the better teams with somewhat similarly-sized stadiums are in one league, then smaller teams with less money are in smaller stadiums, and are usually attached to a pro team. You don't need national leagues with lots of bad teams in them and then a tournament of the better teams only, because only teams which actually can compete are in the top league to begin with.
The major exception to this is football, which just has the pros and college, no minors. I'm not sure why, I don't follow football. Maybe because of the popularity of college football? But on that note, college sports are quite popular in the US, unlike Europe, and obviously that's not something that could be attached to the relegation system. (The largest stadiums in the US aren't pro football stadiums, they are college football stadiums. It's a HUGE thing, particularly in the South and Midwest.) College and minor-league teams are how pro teams get their players.
I've read that the American system of pro sports is actually more "socialist" than the European one, in that things such as revenue sharing, salary caps, and no relegation ensure that all teams have a chance to win, either in the short or long term. In Europe, a few superteams completely dominate, and others really have no chance to challenge them; much less equal.
Multi purpose stadiums serve a public utility and as such it could be argued are worth public funding.
But if its just for one sport for one team its kind of silly.
The good thing about England and their relegation, is that the fans are realllllllllllllly loyal. (Way too loyal really)
Multipurpose stadiums are bad because they aren't ideal for any sport. Hockey + basketball in one arena does work, but baseball + football in one does not, it was tried in the '70s and '80s and was abandoned for a reason. It's particularly bad for the baseball side of things, though it hurts football too I believe. Even soccer wants their own stadiums now, to not have to share with football (grass turf issues, etc.)
Also, cities don't make money off of stadiums; those are always big money-losing projects, every time.
Our pro sports didn't grow from clubs. Our sports were a natural extension of high school and collegiate sports. College has a lot of conference and divisional movement though no true system for it. Think of it more as the old pro wrestling territory system. The pro teams protected each other and shared stars to survive the rough patches and keep the league as a whole alive. Hell before Magic and Bird some NBA Finals couldn't even get live broadcast on TV.
No, football and basketball grew out of colleges, but baseball did grow from clubs. The first professional baseball clubs were established in the US in the 1860s, just a couple of years after the first pro soccer teams in England earlier that decade. That baseball didn't grow out of colleges is probably one of the reasons for baseball's massive minor league system -- for those who don't know, each of the 30 MLB teams has five or, usually, six minor league teams that they own below them, in six levels (rookie, short-season A (short season single-A), A (single-A), Advanced A (Advanced Single-A), AA (Double-A), and AAA (Triple-A). Some players start in college, but many go straight from high school to the minors; baseball is a hard sport to learn, and getting good enough to get to the pros takes time. Back in the 1800s and early 1900s there was more shifting back and forth between "major" and "minor" league status, but by the early 20th century things solidified into a version of the current system of major and minor leagues, because only some leagues could afford to keep up top-level play, and the concept of relegation has never existed in the US.
But yes, for basketball and football the college influence is important.
