Incoming rant: Pro/Rel is a very interesting way to run a sports league. It provides a lot of drama and high stakes for teams at the bottom of the table. It gives fans of lower league teams hope that they too can join the ranks of the elite, simply by earning it. For Americans, the sheer novelty of it can be intoxicating.
It would also cut American soccer off at the knees and would be terrible for the game in the US.
When you look at TV revenues, competition for eyeballs, and general awareness from generic "sports" fans or even soccer fans, it becomes pretty clear that the level of investment that MLS owners make is only sustainable because those investments are protected. For good or ill, MLS is where it is because of a top-down approach, not a grass roots one. Interest in markets has been carefully curated and nurtured, and the number of true die-hards who would stay with their club after a relegation is almost certainly tiny. This is not England where soccer is the dominant club sport by such a large degree that even cricket and rugby are basically afterthoughts, and every team in a halfway reasonable market is a sleeping giant just waiting to galvanize community pride with a "little bit" of investment. In a soccer-mad country, with a hundred clubs full of history and local ties and community engagement, maybe the churn is worthwhile, but in the US you'd just be killing clubs that are relatively healthy with ones that are deeply undercapitalized and unattractive to players anywhere near the level MLS clubs buy now, to say nothing of the media partners.
Pro/rel has its own issues even in Europe, and especially outside England. It tends to erode or preclude other parity enforcing measures as the deeper pockets want to ensure they're never at any particular risk of relegation. It can result in a mid-table liminal space that's every bit as monotonous as the bottom American teams' annual struggles and replaces the very realistic possibility of joy at an unexpected run with mere relief at survival for another year. It also still destroys rosters and erodes support, and particularly outside England it can consign a club to obscurity. Meanwhile, it hasn't stopped the intrusion of money into the game in Europe, and the only REAL way to thrive is to throw money at a promotion effort; there are no more remote factory clubs unearthing a squad of hidden gems and storming up the pyramid.
I'm under no illusions that the American model is truly the result of pure competitive spirit from the owners. American sport is a cartel, moderated by ego and mid-term thinking, not a commune. That said, European sport presents the rather grim (to an American anyway) choice of picking a "big" club to follow or giving up on any realistic hope of cheering for sporting glory. At least in the American system, the oligarchs have decided that a rising tide lifts all boats and that the fans will expect a set of rules that give any well-managed team a chance to compete for the biggest prize. We force MLS to adopt pro/rel, and we'll get a level of investment that accounts for it. That level is unlikely to be anywhere close to current state of the league, which is top 20ish in butts-in-seats, salaries, etc., across 30 teams.
TL;DR: The market for domestic club soccer is what it is in the US, and if you start throwing away huge swaths of it because NYCFC has a down year, you can't replace it by promoting Charleston, romantic as as it may sound, and the owners know that.