Not exactly deep, just something to do with your pokemon other than look at them in your collection. They already have move sets, after all. Just let people be able to have battles against other people.
It doesn't detract from the current game, it doesn't make the game any more arduous for people who just want to collect pokemon, it's just something for those of us who care to have some fun with. There's a spectrum here, from the extreme casual who don't want fights at all, and the extreme hardcore that will travel to different countries to build his ultimate team meta. Adding a battle system allows the game to appeal to both.
the depth of the system is not important, it can be as simple as who has the bigger numbers, the point is that it incentivises improving your collection of pokemon. It gives reason to have different types, to go out and seek more pokemon than what you already have.
It adds to the design philosophy of the game (going outside and walking around), adds to the social aspect of the game (having battles with strangers, creating a social environment), and adds to the longevity of the game (incentivizes improving your team, instead of remaining stagnant with the same 5 or 6 pokemon around your neighborhood).