Allow me to channel my inner Young Sheldon...
For those not in the know, "relegation" means that low-performing teams are demoted into lesser leagues, while the top-performing teams in the lower leagues are promoted into the next-highest league. The best example is the English football/soccer league system: . At the top, you have the "Premier league," which is the only one that most casual fans are aware of. Below that, you have "feeder leagues." At the end of the season, the two bottom-performing teams in the Premier League are "relegated" back to the top-most feeder league, while the two top-most teams in the highest feeder league are sent up to the Premier League.
In contrast, consider the NFL ("American football/football). There, the worst team in the league gets the top draft pick. So, in essence, the worst team gets rewarded for poor performance. So, ironically, the Brits have a system that is way more Capitalist than the Americans, who could arguably have a system called "Socialist."
But those are professional sports and there are other factors that come into play. Im the NFL, the Green Bay Packers, can compete with the Chicago Bears (and have consistently outperformed them for about two decades) because the NFL has a policy called "revenue sharing," where revenue is pooled and distributed across the league. That means a team that is practically based in the ("I've never heard if the town of") Ashwaubenon, WI gets an nearly-equal footing profit-wise as the one from the major market one based in Chicago, IL.
To answer your question, college athletics is not supposed to be about money, at least in theory. Colorado is much less densely populated than Illinois; yet their cross country program has won National Championships. UIC recently finished 23rd at Midwest Regionals. If we had a system of promotion/relegation, that wouldn't necessarily change (for one simple reason: coach Mark Wetmore). But you might see a lot of much smaller market teams who can't afford top talent fall by the wayside and cease to exist. So, no, I don't think a system of promotion/relegation would work. And there is no "draft" in college althletics; success is mostly recruiting-driven. The system, as it stands isn't perfect. But there are serious tradeoffs to the one you proposed.