For blobbies, aguardians, robots, djinns, goats, whatever else might do so. Any item can be fed to this monster, healing a constant amount of HP or scaling to item quality.
Or make the Sample The Local Cuisine cast-able on pets and only then allow them to eat anything You'd still have to deliberate when to feed your pets and when to keep your precious food to yourself, unless you already happen to be a Level 5 Tourist. Which makes sense, I think. Don't have pets if you can't support them, etc
If you're using a skill that actually summons pets, then yes. If you're using the Vegan skill to charm a named monster, you'll want to top off his health every now and then rather than just charming a lowly common Diggle.
The actual intention here is for people to accidentally discover that that enemy blobby just ate the crownstar addendum you were trying to drop, and for healing charmed or insured (or both) monsters.