The limitation on specific flights (if that's the intent) does very little to reduce the health risk and load on cleaning.
To rotate a pet-friendly plane to a no-pets run would need a much deeper clean than the usual tidy-up, even when all pets would be still in their cages.
I'm yet to come across pets in cabin but the bare minimum VA should do is to allocate a specific small segment of the cabin for pets. the last N rows are probably most reasonable, especially when boarding & disembarking happens via rear stairs. That gives a little bit of separation between pets and those who can't be in the same premise with them.
Personally, I'd love to have a pet (one of those hypoallergenic cat breeds which I hopefully would survive or at least manage with it) but can't imagine putting it through the stress of travel in a cage. Somebody please think of the pets' feelings, too...