I guess the mindset is they're trained by that age and also very likely to be at their adult weight, important for communities with size/weight restrictions.
However your mention of not applying this to service or companion animals isn't germane to the topic as they aren't classified as pets to begin with.
I never understood the rationale of no kittens/puppies. After almost 20 years in the biz, I can tell you.... and I'm sure you already know....a poorly cared-for adult animal will do every bit as much damage as a puppy or kitten.
Keep in mind, though, that you cannot set an animal age limit on a companion or service animal.
Our policy was always "dogs had to be over 1 year". We got a lot of pushback, and settled on a compromise. For puppies, we require a pet deposit that is equal to the cost of a carpet replacement (in case of puppy accidents). If the carpets don't need replaced, great. But if they do (we've never had a puppy that didn't leave pee stains) the owners have already paid for the replacement up front, so there's not the shock at move out.
