Not to mention the fact that if one of those companies get infiltrated the attacker will have kernel level access to millions of computers. There is also the fact that some of these anti cheat software are bundled with popular games produced in China.
That would be extremely limiting to do because of the constraints imposed by networked gaming; which requires that some data be locally available to the game locally to allow for immediate feedback.
Just imagine if a web page had to send a network request to control a toggle or to show the contents of an accordion; that's what the game would turn into if this were to be done.
I can build a webcam with an rpi that will play CS better than any human and only communicate with the gaming PC through a mouse and keyboard.
Anti-cheat systems need to look for movements that are super human, no rootkits required.