With FSD-on-city-streets, that's more-or-less what happens. I'm on that beta, and something like what
@Mashina reported happened to me a week or two ago, only I was in the left-turn lane and the straight-ahead lane's light turned green while mine remained red. The car proceeded to start moving forward (as it should have when the light changed, but of course it had not -- at least, not for my left-turn lane). Fortunately, I was alert enough to stop the car before it moved very far, so no harm was done. Tesla warns that the FSD-on-city-streets functionality requires constant driver attention, and they aren't kidding about that; drivers should be alert, even when the car is stopped at a light.