This has been a problem since C&D came out. I think it was an unintended consequence. I agree with what a lot of simmers have said here; I don't want all the sick pets to go away, but I'd like to see it toned down. I've had the same problem as the OP, where I'm playing a family with a pet who is well cared for, and a few hours later when I'm playing a different household, I'll see that pet being walked by their owner and they're somehow sick and dirty all ready. It's ridiculous. I understand why stray pets might have that issue, but not pets who have owners.
I've taken to having my sims who own pets (because they often take care of strays as well) buy a bunch of the wellness treats. Usually you can give them to strays as well and it heals them, at least in my experience. It has been a while since I've done that though, so I don't know if it still holds true. I really hope this gets a permanent fix at some point in the future.
