[@Izuriel Steam] Two reasons besides fighting off wild pokemon. One similair to martial arts combat is a great way to teach discipline and exercise. These pokemon need to be capable of some rather grand feats and battling skills aid that. It teaches moves and works as a great teamwork exercise between trainer and pokemon.

The second reason is that the trainers are also the police force of the cities. Not everything has been perfect everywhere. Food get's scarce people get desperate things can still be scary despite how well off things are right now. There are also groups of less valiant intentions. Not everyone still on Earth is a great person.

I do want you to realize though that wild pokemon are a major danger though. If you wander into an agron's nest you are screwed unless your pokemon can subdue it or at least make it back off (same in reverse sometimes pokemon come into town smelling food or something). As I've said above pokemon are wild monsters yes they can be tamed, but a wild pokemon will go on instinct and that usually involves viciously attacking anything nearby.