Most people don't care what the other person thinks about their email so long as their boss thinks they are doing their job (and their boss is usually the one paying/telling them to use AI) and the other side responds. Should they? Probably, but everyone should probably do a lot of things we don't.
I feel a tinge when I see an AI written email that is longer than it needs to be/boring to read but I still need to engage whatever it was they were emailing about anyways.