Seems like this policy would apply pretty well regardless of who/what generated the code.

YES! "No AI" policies that are purely based on technical grounds make no sense to me. Bad PR's are bad PR's regardless of their source.

Are we really in a situation where good code that solves a problem won't be merged because the person the person checked the "I used AI" box on the PR?

Ban PR's that are too big, don't have a clear purpose, touch too many areas, etc.