What about cheetahs and lions and things like that?

Too volatile. 

I can see the appeal - after all it was big in circuses with all the big cat trainers. But in an environment such as this one, you need to be 100% sure that the animals will obey you. There can't be any margin for error - which there would be with animals that look at you as if you're a walking menu. Just because they obey the trainer doesn't mean they won't try and maul you to death the moment said trainer isn't looking.