To put it very simply, the 'kernel' has significant control over your OS as it essentially runs above everything else in terms of system privileges.
It can (but not always) run at startup, so this means if you install a game with kernel-level anticheat, the moment your system turns on, the game's publisher can have software running on your system that can restrict the installation of a particular driver, stop certain software from running, or, even insidiously spy on your system's activity if they wished to. (and reverse-engineering the code to figure out if they are spying on you is a felony because of DRM-related laws)
It basically means trusting every single game publisher with kernel-level anticheat in their games to have a full view into your system, and the ability to effectively control it, without any legal recourse or transparency, all to try (and usually fail) to stop cheating in games.