While it is probable that some will dope in the clean league, a simple matter of instituting lifetime bans and reclassifying any and all records held by an athlete would put a strong disincentive.
As to your unsupported statement that all the fame and prestige will be associated with the clean league, that is a matter of marketing. If there wasn't a market for doped up, super-humans athletes professional sports would be very different. Look at WWE, it's not even really a sport, but it takes in half a billion dollars a year on the promise of watching steroid guzzling guys throw each other around.
For many people the problem with PED is the dishonesty, the unfair advantage it gives a cheat. But when the stigma of cheating is lifted, all that changes.
A more likely outcome is that fans of some sports would shun PED and unlimited league events, others would see it as a natural extension of their attitudes about competition.
https://www.wired.com/2012/09/sports-and-doping/