Well I was thinking more local multiplayer for genres like fighting, first-person shooter, third-person shooter, racing, kart racer, platformer, brawler or party. Trying to do local multiplayer for an MMO would be a disaster.
Local multiplayer restricts the possibilites of finding people to match and hone your skills, especially if you aim to be a pro player. You are simply isolated from the community, depending on your close friends to play with (witch is terrible because it could happen that nobody within your circle likes the game you want to play). Being online allows you to access the whole community worldwide, plus being able to find players with similar skills to you for more even, fair matchers.