Drafting a QB in the top 50 picks and not starting him immediately is a recipe for disaster IMO. The fans, the players and specifically Baker knows that a team isn't drafting a guy that early without the expectation that he becomes the starter eventually (if not immediately).
Baker will get booed off the field with every incompletion if the fans think there's a better option on the bench (and I'm not saying a 2nd round rookie would be a better option, but the perception would absolutely be "this guy can't be worse!" if Baker struggled). Hell, the fans are already restless this year and friggin completely washed Keenum is the guy who would be replacing Baker.
And this shift would happen immediately, like drive 1 of week 1. Mayfield would have to play great from the jump or the fans would absolutely turn on him and things would blow up IMO.
We just saw this play out with Eagles and Wentz. They drafted Hurts and the fans were immediately clamoring for him as Wentz played progressively more and more like crap. The Eagles had a horrible season and ended up firing their coach over it too.
If Baker is the best option for the Browns at QB for 2022, then there needs to be no competition. Put the full support of the organization behind him and roll the dice that his injuries are the reason he's struggled this year. If he stays healthy and he still fails, then you just move on after next season.