There are some. For example extraction shooters kinda lose a core aspect of its genre because the player interactions are built on the idea that you don't know who the other groups in the server are. Are they hostile? Are they friendly? Will they stab me in the back or help me out? How many are in a group? Technically it would be possible to set up community servers (if you had access to the server software) but if your community plays on the same server you kinda lose that uncertainty of who you're going to meet, because you know the people you're playing with.

Another one IMO that benefit from matchmaking are 1v1 games. Chess or fighting games or anything of the sorts. Community servers would be moot because you can only have 2 people in a match. You could probably build a tournament style community server but it wouldn't add much value. I think matchmaking makes much more sense there.

There might be more but I think that list will be relatively short and in general most games would probably benefit more from having community servers.

My point is mobas aren't really that feasible with community servers, are they?

There's still a bunch of customs. Most are private.

I really don't understand what one sees bad with a central server, because the function those community servers served is now served by discord servers, basically, to which you can go to find gaming company at the drop of a hat. But there's not the same limitation of "oh we're not on the same server", except for ofc zones which still exist, America, Europe, Asia, etc.

Oh "even mmos"? Those have existed since I can remember. And I started online in about 2003.

Why'd you'd want a private server for League for example?

This is everything I meant to convey with my "lol?" but I realised it wouldn't be conveyed and still did it because I was too lazy to write this