Most amateur leagues that do form around a game do use these kinds of features it may need to actually phone the home servers but online leagues generally just use default game functionality. I don't know any game that's worth playing competitively that doesn't have a feature for a 'custom game' or invite-only game. If it's worth playing competitively usually a group will spring up- it can be a hundred people or hundreds of thousands of people but those communities do exist from everything from soldat to Dota 2. You just have to go find them. Generally you don't start with a full team either, you play pugs (pick up games) and start to learn the competitive ropes just like you would in a more traditional game.
The downfall is unlike older titles where individuals rented servers and communities grew around servers easily, the lazy matchmaking that you can do nowadays makes actually meeting people you want to play with much harder than it used to be. You can play 10 hours in a matchmaking competitive game and never play with the same people twice, whereas you usually were playing with/against the same people all for at least an hour or two at a time. It's not impossible to do just is less organic to find people you want to play with at their worst and at their best.