I could never understand this, really.
Before achievements were released, pets meant absolutely nothing for me. The only point in time when I actually started caring about pets is when pet battles got released (although maybe the reason was because the actual gameplay was worse then).
I see people trying to sell pets in Trade channel all the time and I just ask myself “why?”. Why would I see a useless NPC that does nothing but run after me and annoy me as a status symbol? Is it pretty? Does it buff me? Does it help me in battle? Does it have any interactions? Does it do anything at all?
No, no, no, no, and no. On top of that, it takes a slot in my bags.