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There are definitely class pets that are done well.
I had classes in high school with huge tanks that were full of plant life, with a few fish swimming around in them.  The fish never had any health issues, they had lots of hiding spaces, it was a great example of how much space and plant life is truly needed for an aquarium to thrive.
Where I worked, we weren’t allowed to have class pets unless they were our own personal pets, and they passed a whole bunch of screenings.  We had to prove we had adequate habitats for them in the classroom (no tiny cages or [god forbid] carriers).  We had to submit a proper diet for them, so that management knew they were being fed properly and could order food for them.  We had to clean their habitat regularly (I never worked in a room with a pet, so I don’t know how regularly).  The cleaning was a big one, since we had room inspections all the time.  Pets were not allowed to be left overnight (with the exception of fish, which still had to be brought home for the weekend).  The pets had to be registered with the local vet and taken for regular checkups.
One of my coworkers had a Guinea pig that was absolutely pampered.  Huge habitat at school, and a whole room at home with her.
I had to read this 3 times to understand what you meant. I should really start drinking less. 
At first, I, for some reason, assumed "class pets" meant high-class pets, as in fancy breeds of cats or owning a white tiger type of thing. Then, I thought "class pets" meant teacher's pet/favourite student but the whole post still didn't make sense. THEN I realised that class pets were just class pets all along. Pets (animals) that are shown/brought to a class of children. 
I need a new brain.