I honestly love hate the idea. Why not just store your pet in the computer when it's not in use? But Spot and Grudge cause minimal problems just hanging out, so that doesn't really seem to be a *large* problem. Maybe it's worse if you don't have your own personal quarters. I actually wouldn't have thought that storing a pet inside the transporter buffer like Mbenga's kid would be inherently cruel or disturbing but you've somehow made it terrible and I love it.
Even if it wasn't a technological limitation (cause, let's be real here: the transporter replicates living material all the ******* time.) then it's certainly an ethical one. Why would you even need to replicate a pet anyway? Plenty of living animals out there: and the pain of loss is an integral part of living and maturing.
I actually don't agree? Pets that human people have in the present all derive from the pet trade. Shelter animals are the descendants of animals that were pets, the results of abandonment, failure to sterilize, or excesses in the pet trade itself. I don't think in the Federation's utopia that exists on Earth and within starships and stations there
are any feral animals. There would only be pets already being bred to be used as pets. (Sterilized at the nursery and fully GMO-certified.) So at that point, it's an ethical wash whether you bred them or replicated them. Animals taken from the wild, on the other hand, are undomesticated and do not thrive in captivity, and they're pilfered from an existing ecosystem, which feels out of line with Starfleet nonintervention and ideals of self-determination among other things.
Technically though you should already be able to have the next best thing in Picard era, because ubiquitous holography and AI pets have both been established as things. "Computer, activate Emergency Cuddle Hologram." To me this seems the simplest solution to the problem. Even if you don't have holo-emitters in walls in a particular ship or home, they seem to have been miniaturized over the years to make that integration possible, and the power use is not extreme. I imagine you could at the very least have a standard Starfleet briefcase worth of kit that produces a fully thinking and feeling pet on command.
It was definitely established in TNG that living tissue couldn't be replicated and I always *thought* that was a technical limitation. It seemed consistent with the fact that people routinely refer to "programming" replicator patterns and this seems to be an involved process. You can't put a bowl of dad's gumbo on a transporter pad and replicate it whenever you want. I've always kind of assumed as I've said before that the meat was already Implausible Targ and quite distant from functioning living flesh.
In Deep Space Nine though, something different happens in "Our Man Bashir": when Sisko et al. suddenly have to be stored in a computer somewhere as transporter patterns, the station sends their bodies to the holosuite computer, but has to overwrite everything else on the station to store the explicitly quantum information of their brain patterns. So is it living things or just brains that can't be stored as data and replicated? (Worth saying that you can handwave information that can't be copied, only transferred, by throwing "quantum" at it, because there is such a state in a quantum computer that can't be read without being destroyed in one place and recreated in just one other. But if human bodies aren't quantum patterns, they shouldn't have this limitation, and neither should any living tissue inside them.)
Single-episode miracles probably don't establish real facts about the Trek universe that can be depended upon elsewhere. But even if living bodies can be easily produced from information that fits on a holosuite computer, the brain information of a dog would be a significant fraction of that of a human, which would be a large amount of data that might be inconvenient to store, much more than a hologram AI.
So I'd go with the holo suitcase myself. It's less speculative and has all the convenience of a replicated pet you store in the computer, though without the hilarious squick.
Thanks for the assist on my reply to Fero, Axaday.