It's cheaper to install malware.

That's all there is to it: cost.

Not how it works, and it is a huge science behind it all. First of all, you don't want false positives. People would ruin your game for it. The reviews would be awful and it would breed more cheaters (angry at a game that banned you for no reason? Make it ban you for a reason, ruining people's fun in the process and costing them money). Second, most of what you are talking about is already done on server side. Third, the concept of banwaves is a thing. You want to catch as many cheaters at once with a single detected cheat. If you ban someone at first sight, the cheatmaker will refund that first person and think up something worse immediately. If you ban 30k people, all of them flock to the cheatmaker asking for refunds. Which he can't obviously provide, since they already spent that money over the course of the time the cheat was active, etc. Fourth, lots of cheats are subtle enough to be "invisible" to any sort of detection. Guy has an overlay that shows people through walls. You can't ban overlays and the client needs to know where people are on the server, it just hides them. All you can see is what a human would see - a guy looking at people through walls, but trying to hide it. A guy with "incredible gamesense" basing their tactics on info he couldn't have gotten. A moderator that knows what to look for would see it. An admin that abuses power and bans everyone that's too highly skilled would also ban the cheater. But try writing anything that checks for the "averages" and you ban actually good players that use sound, etc. Same thing with aimbot - it's very obvious to someone looking at gameplay. But going off of statistics you ban everyone who "has a good day".

The way to do it, was how Valve handled it in CSGO. No idea if the system is still in. They basically tasked their community with being the judge and executioner. They would send you a replay in client, showing you 10 mins of the match. Sometimes they would send you a replay that they already know has a blatant cheater in it, to test if you actually say "ban" if you see one. They scored the judges, valuing better ones more and providing feedback saying "your case has banned a cheater". It was a slow process, but effective, or at least it would be if the game wasn't so incredibly popular and free. Obviously a live moderator would help a lot, but it's the next best thing.