On the old map, I accidently went to spawn once and forgot to sit my dog down before tping. Didn't even realize it was mine until I noticed it was following me around. Someone quickly named it Stinky, or something to that effect, with a nametag, and then someone else killed it 30 seconds later. Despite it being on accident, I deserved it, I brought it there and I should have known better and taken more care before tping. If you really want your pet to stay alive, then don't leave it randomly in the open or in a public place. Would you leave a real life dog just sitting in a town square?
There's absolutely no reason worth having to deal with the extra lag from protecting them, especially if it's your own negligence concerning your pet's safety. Just leave them at your base, you'll only be gone a few minutes, they won't get upset.