Ames: I believe it’s not the putting the dishes in that’s the problem, but the rinsing of the dishes.
I think it’s similar to the fact that some people won’t clean up after Seudah Shelishit. It’s like they’re preparing for Motza’eh Shabbat. (But I was told–not by a Rabbi–that if you’re the type that a mess or dirty dishes would bother you, you can.)