I think I've had too many of the wrong GMs. You say animal companion, I see a companion my character can build an emotional connection with, and care for, who isn't my team... And is inevitably doomed to kark it messily when the GM decides I need more drama and pathos in my characters life.
I tend to avoid films where the dog (or cat) dies. How much worse when it belongs to a character I'm actually running. I may be an old softy.
That's part of the problem

I have seen some YUGE explosions over 'pets' caught in well... explosions....
Some players will freak out that 'Mr. Fluffy' becomes a target for damage... regardless of if 'Mr.fluffy' is a tabby cat hiding under the runner's jacket, or a Cerebus hound currently chewing on an Mook's head...
Which in turn leads some GMs to just say 'Nope. Not MY table'
I'm not against critter companions per say, but that means they are LEGAL targets in combat (as called for).... or Dinner for that Triad boss you just piss off...
( Triad Boss: "Ah Mr. Runner, we are most displeased with your actions that cost us considerable time and effort. But let us be reasonable and about this over dinner. "
A plate is set down in of the player with a fully cooked hunch of meat on it, all professionally prepared
Triad Boss: "This is my favorite dish from Korea, I was so happy when Mr.Gao joined us, as finding someone who can cook Cat in the traditional manner is so very hard here in America. But I am prattlingly on... please; Enjoy your Mr.Fluffy while its still hot."