Gonna get on the spitballin' train. What would people think of trainer abilities? Like a boost to your team, depending on bond strength? THink advance wars, something like a boost to speed for your pokes or a boost to defense.
Either that, or it's like mentioned earlier, pokes get stronger as their happiness gets higher. It would help balance out some pokes/make it harder to level hard to train things like gyarados, but make stuff that's quick to love like wigglytuff, more powerful early on.