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.
Plenty of modern community servers still do the same. Face-it servers for Counter-Strike 2 will have additional anticheat, not less. Modded Grand Theft Auto V servers, FiveM, built their own anticheat they call adhesive before RockStar ever added anticheat to the full game, and this prevents it from running on Linux to this day.
I play at moderately high elo in Counter Strike (Faceit Level 10, 25k Premier) in a lesser populated region and even Valve matchmaking is mostly fine. I have a multi-thousand dollar inventory, old Steam account and over 7,000 hours in Counter Strike, all of these things (likely) impact my trust factor.
Trust Factor doesn't detect cheaters, but it sure does expose me to way way less cheaters. It's pretty uncommon to see an obvious cheater in CS2, the number of closet cheaters likely increased. In CS:GO rage cheaters were more common, but they are (for the most part) detected a little bit better now.
Cheaters using external tools in Dota are rare. Smurfs are a much bigger problem than scripters/maphackers.
In my experience, MW and CS aren't that bad. I see a cheater only about once in 20 games.
I also play online chess. No kernel level anticheat is going to help you there.