American sport has developed just fine without it

That depends what you mean by "just fine".

The lack of lower leagues is a big problem for US sports. It has led to universities becoming amateur leagues that develop professional athletes, however they're "amateur" only because the labour of the athletes is exploited. The athletes aren't paid, but the coaches are highly paid, and the athletics programs are lucrative for the universities. That has led to all kinds of problems.

for MLS in particular there is no massive surplus of clubs and investors itching to to take a crack at that sweet MLS AppleTV money

Of course there are. That's why people are having to pay hundreds of millions to get an MLS franchise. NYCFC had to pay $100m to join. FC Cincinnati and Nashville SC each had to pay $150m. MLS has announced that the 28th and 29th teams will have to pay $200m to join, and the 30th will have to pay $325m. It's a system that benefits the existing owners. Nobody's going to pay $325m to enter a closed league just for the vanity. They expect to make that money back, which they can do because a closed league is lucrative for the people who get in. You can bet that the owners of the team paying $325m to join the league are going to vote to milk the next team that wants to enter for half a billion if they can do it.

In a system with promotion or relegation, it can be very expensive to buy a top team, but you can buy a lower league team, manage them well, get promoted and get into the league that way. If you wanted to, you could even start a brand new team and pay nothing. You'd have to enter at the bottom of the pyramid and work your way up, but nobody could stop you.

like drafts (almost irrelevant in MLS these days, btw) and playoffs are the particularly American solutions to maintaining interest throughout a season

Which they have to do, because without the danger of relegation, it's boring! The attempt to enforce parity also makes it boring, because if a team is having a bad year, you can tune out, come back in a season, and everything will be shaken up. Nobody in European leagues needs to implement silly things to make the league more interesting because the danger of relegation (and the thrill of promotion) is enough to keep people interested.

the American leagues are no more “boring” than the EPL

Of course they are. That's why so many people watch the Premier League despite the awkward schedule. If MLS were just as exciting as the Premier League, nobody would do that.

Most of that is due to the local players being significantly worse than their European counterparts, but it's also because the league structure makes for boring, meaningless games. Yes, the threat of relegation is stressful for fans, but that stress is excitement. And, relegation can even be good for fans. For a club that is consistently near the bottom and always in danger of relegation, relegation can be refreshing. It means a season where their club is powerful compared to their rivals, not weak. It means going from a record of mostly losses, to being able to expect a record of mostly wins. Sometimes it's better to be the big fish in a small pond (a club that's regularly at the top of the 2nd tier league) rather than a small fish in a big pond.

the EPL is a needlessly cruel exercise in hopelessness, where your budget is your fate

The budget has a lot to do with a club's fate in the Premier League, but it's not everything. That's how Leicester managed to win a few years ago. It's also apparent in how Arsenal went from being a rich club playing in the Champions League year after year, to being a bloated, mismanaged club struggling to make any European competition at all, to then being a leaner, focused club challenging Manchester City for the title. A small club like Brighton would have to spend years building up a fanbase, expanding a stadium, etc. to have the revenue to compete with the clubs at the top of the table. But, by being well managed they've managed to make it into the Europa League on a budget much smaller than Chelsea and Tottenham. That's one of the things that makes the Premier League exciting. A well run underdog club can make a run for trophies while a rich but badly run club can be in danger of relegation.

there is no groundswell of clubs and investors across the US itching to build 20k seaters

Yes, for investors it's a bad deal. The closed cartels of American sports are much better for investors because they can't fail too badly. Mismanage their clubs so badly that they finish last, and they get the #1 draft picks the following year. No investor would want to buy into a system with promotion or relegation if they had to choose, because then they're in a cut-throat world where they have a real danger of failing.

Also, the whole point of a promotion and relegation system is that you don't have to start with a 20k seat stadium. You can build some small bleachers seating a few hundred people, then grow from there. If there's enough interest that you're regularly selling out, you can expand. More fans in seats means more revenue. More revenue means more money to invest in the squad. More investment means more success. More success means promotion. A club can grow until they can justify a 20k seat stadium based on consistently selling out their 10k seat stadium. With a closed system like MLS the crowds need to be "MLS sized" from day one, so it's a big risk if there simply aren't enough people who are interested.

it’s unfair to the people who do enjoy American sports to say they’ve got it all wrong.

The people who enjoy American sports would enjoy them more if there were promotion and relegation in place. They've just never been lucky enough to experience that. They're stuck watching sports run by owner-managed cartels.