This doesn't necessarily even need a mechanical benefit, though if bundled into a pokemon care update could be used to increase happiness by a small amount. Currently there doesn't really feel like any special connection is made between a trainer and their pokemon, and the only real reason to have one out is for field moves or showing off.
Starting off, I think just the ability to feed a pokemon and have it play a small animation (like heart particles and hopping) would make the pokemon feel a lot closer to being a creature than a tool, and is not a deviation from core pokemon game style as many recent titles lean heavily towards this sort of feature.