i know its not that important compare to other suggestions.. but how about treating pokemons as a pet for real? like feeding them every time they hungry, letting them play inside your secret base, etc..
how it works:
it only happen when you put the pokemon outside of its pokeball/pc box, the pokemon will soon request for something like it wants food.. or maybe it want some hug :D
*you can put out all 6 if you are inside of your secret base..
* you can only put out 1 pokemon if youre outside of your secret base
* i think of it like a minigame where you doesnt lose anything