The only way Youtube could do that is by making a Google account required to watch videos. Logged out users on Youtube’s official services like its website and mobile app use the same API these frontends use, so breaking that API would disable its actual services for users without an account as well. You’ll notice that you cannot perform any logged in actions with a Google account on these frontends, and that’s because the frontends only use endpoints that don’t require authentication like watching videos and reading comments. This is the same reason why Twitter hasn’t shut down Nitter (the privacy frontend for Twitter) yet, even though they would really want to.