Why? I have a hard time imagining anyone would care more about the integrity of the game than the community. Private servers are an IP play, allowing companies to pull the plug completely when it is convenient for them.

Say you've got a game that's specifically designed for 5v5 play. In this game, things become imbalanced and overly chaotic when there's more than that many players, the main game mechanics start to fall apart.

So now let's say you only have private servers. A bunch of 10-seat servers, and each match takes ~30-40 minutes. How does this work in practice? You have servers with like 8 or 9 players sitting around waiting, hoping for someone to join. How long will they sit there waiting? We potentially have hundreds of these partially filled servers waiting for other players to join. Wouldn't it be nice if there was some system that would automatically send people towards your nearly full server? Some kind of...matchmaking system?

How do we ensure somewhat even levels of skill among those players? Some kind of system that tracked past performance against players of other skill levels and could help you find other players around your skill level? Some kind of service to help you find matches, like some kind of...matchmaking service?

Not all games need matchmaking services, I agree. A lot of games do benefit considerably from having matchmaking services.