Depends on the game, really, but “relying” on anti-cheat is pretty common. Larger games tend to have teams who review cases that get flagged by the systems and players and do manual removal but these teams also tend to be quite small and unable to adequately handle the amount of cheating that occurs.
If gamers want to see cheaters less often, they need to pressure the companies to do human moderation in addition.
I’d argue the same, actually. It takes people to moderate people and dedicated servers make it easiest. Modern match made games could still have admins, the company needs to pay for them.