SB Nation runs a relegation simulation from 2005 - 2012 similar to EPL rules.....
...because of recruiting. No kid with an offer from a school with little to no chance of relegation would, in their right mind, take a chance on a school that might be relegated. Plus, the difference in money is so vast that athletic departments couldn't function. You can't go from getting $20 mill from your conference to $500k or whatever the difference might be. State and Ole Miss make it because of the subsidies from the league. Being in the SEC is everything to us. Plus, the stakes are already high enough - people are willing to lie, cheat, and steal for their school to have sustained success. Imagine what they would do if it meant relegation.
And correct me if I am wrong, but don't the same teams usually win the EPL - for example a team that bounces between Tier 1 and Tier 2 rarely has a chance to beat Arsenal, ManU, etc?