Rivals in new games

I always thought of rivals as annoying encounters, why not have them on the map they are free roaming on cities and routes. You end up encountering them hunting a legendary or items near by giving you hints on where to locate them or a random battle where their pokemon match the level and amount of pokemon you carry with some being swapped out by region you find them in. It would revise them and make them more of a rival then a annoyance always in the way