If you were to want to ban a thing like gen ai you would need to clearly define what you mean by gen ai and why you would want to ban it.
If it boils down to banning computer assisted creation of things, that is hard to argue, since already digital art creation is a lot different from analog creation of the same art. People just could not be bothered to develop the skills to do it with ink and brush. They just click buttons to draw a circle. They can even undo their mistakes, unlike drawing on paper. Or just look at a photographer that does not even draw at all, but creates a picture by just capturing what is there - and later modifying it with digital tools.
If it is by source of learning materials, that is an easier case and actually part of the reasoning behind mandatory asset tagging on Itch. There is ambiguity and discussion about copyright, legality and whatnot. But this is also short sighted, because in the future there could be computer systems that output the same workload by other means. Other training material. Procedural generation. Actual intelligent systems that actually learned. Whatever. Does not matter.
If it is a site ban, that is the easiest to argue and there is a lot of precedent in terms of quality arguing. Itch has an arbitrary file number limit in web games for this very reason. And a lot of ai gen creations look not really good and can be put out very fast, so overal quality can suffer. On the other hand, overall quality on the lower end of popularity ranking is, well, lower. All without help of ai. Humans do not need ai to create bad art in games.
What I see in practise in the indie sector is games being created by people not having a budget or talent for doing art, but for creating a game. So it enables them to create a game. Just as the existence of game engines like Godot does. They can partake in that hobby. It is not overcoming a disability, but it is overcoming a barrier.
For games in particular, things like rpg maker do enable hobby creators to put out games far more, than gen ai images do, in my opinion. So if we prevent ai slop on Itch, why stop at ai slop. There is regular slop as well.