I suggested a quick dirty fix but i am not that sure anymore. You have a lot of stuff dependent on that driver (cuda vaapi utils etc.). We can purge them all of course, and then you would be able to unistall the driver, but we are actually still not sure if that is the problem. Collecting logs as suggested before would be the better option. So more competent people than me can see why exactly X server or whatever fails.
If you want to continue to blindly try to remove the propitiery nvidia and see what happens, then it would be
sudo pacman -Rd nvidia-utils cuda nvidia-vaapi-driver-git
But it is a dangerous path, trying to fix with wild guess without actually knowing the problem. Consider doing it the right way - boot from live usb, chroot, post inxi and journalctl etc. One of the tutorials is already linked above, the other would be