Yes, but that exponentially increases ongoing costs for hosting servers for the game to perform those extra checks, and unless you're one of the Valves of the world, you aren't going to have enough data for an automated system to work properly.

Counter Strike effectively has had a server-sided anticheat since the latter half of Global Offensive's lifespan, but there are simply too many gaps in the armor - difficult to determine what counts as a violation with 99% certainty, false positives, automated peripherals used by players that "copy" real human players, and so on.

In a perfect world, the answer to this problem would be community hosted servers ran by independent admins who could audit player activity and exercise human judgements. But that would severely limit the scale of games like the Finals, since both those who could stomach the cost of hosting and the quality of matchmaking would diminish. Even after those measures, it's not bulletproof. Ask RUST players, TF2 players, DayZ/Arma players, and so forth.

Windows users are far more likely to be technically naive enough to install a cheat that will be detected by the kernel level anticheat, and the existence will also act as a deterrent and price increase on the cheat maker's side. The subset of Linux users who desire to cheat may not be affected by those changes, but other methods, like reporting, active memory checks, and pattern detection can still keep fair play.

This can't just be a one stop solution. It has to be hybrid. Otherwise the scale of PVP multi-player games we see today is impossible to maintain.