Unlikely, local multiplayer doesn't work for MMOs, for example. Not to mention modern online games with focus on competitive/e-sport scene have a database system and algorithms that make sure players with low skill doesn't match against high skilled players. The matchmaking algorithms are responsible for providing even ranked competitve matches and are a huge deal. They make sure that newbies will likely match against newbies and top players will likely match agains top players, this is the biggest bennefit of dedicated servers.
I remember in the early 2000s when I played online games like via descentralized p2p connections, like CS and Quake 3, it was very frustating for you to manually enter a game and find out all players in that game were much better skilled than you, leaving you eating dust, being killed all the time. It just pull new low skill players away.
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 nobody you know like 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.