I get what you are saying, I remember the days struggling with firewalls and NAT, with tools like hamachi... but I think you were responding to the stage of online games that came after that - private servers you generally had hosted by a provider.
Best of both worlds, community run, unique so communities would form around servers, and can't be obsoleted.
Downside is matchmaking isn't as good, but oh well.
Communities often formed "leagues" you could compete in. You could join teams for team games and teams were ranked, had matches, competed. For more single oriented things you were your own matchmaker: choose the servers with more skilled players. Different skillsets naturally tended to gravitate to specific servers because they knew they could compete with other skilled players.
But you could find a group you enjoyed playing with and learn from them. I spent hundreds of hours in a UT2k4 server in Team Arena Mode warmup just practicing air rockets, shock combos, and flick lightning gun headshots. RIP UT2k4
Matchmaking feels like it's a really effective optimisation, but of the wrong metric. It's trying to match you up with players of the same skill level in a reasonably short amount of time. I think I place higher value on seeing a familiar set of players, and gain a greater sense of achievement from rising in skill within that set than from rising in global rank.
Best of both worlds, community run, unique so communities would form around servers, and can't be obsoleted.
Downside is matchmaking isn't as good, but oh well.