SalaBimSim there is a way to take pets to a Uni campus. Some lots on campus can be changed to Residential. That's how I've got it to work. So, Briny Tower on the Foxbury campus is perfect for this. I converted it to residential, still with individual spaces for roommates. My Sims have lived there with dogs and cats with no problems except that the dogs have to be called outside to go potty. I add a locked door next to the elevator to stop other students wandering in. In Britechester I use Darkwing House switched to Residential which is ideal for a solo Sim with pets and optional roommates.
I absolutely agree about strays, it's so glitchy and what frustrates me is that you can't invite the stray to your house and adopt it from there. The Adopt option only appears at certain spots in Brindleton Bay, Moonwood Mill or Selvadorada. So I make pet rescues with private vet offices run by the lot owner. I add the Cat/Dog Hangout Traits and make places for food, sleep, toys and training. My Sims tend to them as a vet and train them. Other Sims can visit and adopt pets. I give my Sims the self employed job of Vet or pet trainer using Register with the Ministry of Labor. By doing it this way it doesn't get loads of Sims wandering in like a proper business would because the visiting animals keep my Sims busy enough, instead I can visit with other played households.
In terms of improvements I'd like to see more breeds, more realistic proportions for dogs like Dachshunds, improved dog walks and pets sleeping instead of getting falling over tired and hitting the floor from exhaustion. I'd like some more collar and harness options for small dogs especially. Short haired breeds should all have pet coats for winter temperatures. I'd like to see playing in/drinking from puddles reduced too. I've had several dogs and cats IRL but none of them have ever bothered with puddles. If there's water on the floor my cat would yell at me to clean it up, he'd never go near it!