The problem here is not itch.io but the payment processors. itch.io is as much a victim as the game developers. If the processors block payments to itch.io then itch.io cannot pay any of the developers, so had to do something.
Any other platform will eventually face the same problem.
itch.io is a tiny company, so lacks the resources to quickly audit even just the adult content present. It is, at least, trying to support all of its customers. Uni and many others are still here, even if not searchable.
I'm not saying to not try other platforms, only that itch.io is trying to be supportive.