They already do this. Including peripherals which appear as an actual mouse, but they are there only so that cheat software can take control of the input without modifying the game memory. There are cheats which run on a separate machine and access the game memory via a dedicated DMA card (which itself presents itself as an innocent piece of hardware). Note, this can still be detected either via detecting the DMA card itself, or eventually these shenanigans will be killed off by IOMMU.

Unfortunately, there are also plenty of offerings which do not touch the game memory or process at all, and work purely based on image recognition and these days they actually use AI that is trained on specific games. I have no idea how they plan to detect these. All the cheat needs is the video feed and the ability to provide input via mouse and keyboard, and as you say this is trivial to do in a way that is entirely undetectable.