My DNieces had this in their school for a couple of years. It does seem like a bit of a cheek! I’d happily take my cat to an office job, but feel that would be frowned on! If you have a class hamster or gerbil, it’s safely in its cage most of the time so you can get used to it or ignore it.
I remember my DB saying at the time that the school really wanted the head, and the dealbreaker for him was bringing the dog to work – so they agreed to it to get him.
One of the DNieces in particular is terrified of dogs, whilst the other one is a bit braver (and doesn't meet dogs that much). They would talk about the dog a lot - they were obviously fascinated by her; about her barking when they walked up to the school in the mornings (we talked re why dogs do that), about her coming in to the classroom and taking their friend’s dress in her mouth…(in a gentle way, from the sounds of it, but it made an impression! Depends if the dog bounded in or was brought in on a lead... No idea).
I was torn between thinking 'great, the exposure will help them' (I was scared of dogs as a child - we didn't have any pets or know anyone with a dog - and their Mum is scared of animals so all they manage is a hamster), and worrying about how they were being distracted from learning by fear.
(Head got sacked a couple of years later, so problem solved).