You can bandage your pets out of combat with low veterinary skill just fine. In combat pet healing I wouldn't try anyways (at least with veterinary).
I run a Thursar with 100 Creature Control + 100 Advanced creature control as my PVE farming build. I usually take 2 lvl 24 blackbears. People usually undererstimate them and almost ignore them. For PVP you probably want to take stronger pet e.g. a Terror Bird.
It's far away from a mainstream build, but it is viable. You usually want to hide your pets somewhere, lure your enemy into meele combat, and then send the pet as addition on top of it (or onto the mage, in case they got one).