Getting pets from chocolate frog collections

In the last chocolate frog collection I completed, I got a cornish pixie. I also have a pet pygmy puff that I never adopted and have always been confused about how it got there but never realised until now. I don't think that when you complete a chocolate frog card collection you should be able to get pets. I have obviously accepted both these animals and found an IG way to explain their random appearance but I think that not everyone wants the responsibility/inconvenience of a pet they weren't expecting.

Since it isn't possible to gift people pets, I don't think it should be possible to win them either.