Consider that in Return the enemies resets if you go back to previous rooms and if I'm not wrong, there is no way to visit a rooms just once if you go for all. So for that reason alone, you need to be more specific, since there is technically an infinite amount of enemies.
That technicality aside, I don't think it adds anything to the board or elevates the run. I don't see any value from a speedrun perspective since the run would be in fact very much slowed down due to all the hunting you have to do.
It might be a neat challenge run and you can still do that if you want of course. Play the game the way you want. That's what self made challenges are there for.
I agree with Bronkel here, and there's possible spawning issues like the bats in 'be prepared' you would have to think about. Saying that, if you wanted to show a completed run of it and if there's a few people who would show intent of running we could go from there.
