Even putting aside the logistical impossibility and massive political difficulties of vaccinating everyone, there's a good chance it still wouldn't be enough to

Even putting aside the logistical impossibility and massive political difficulties of vaccinating everyone, there's a good chance it still wouldn't be enough to eradicate the virus. If herd immunity needs say 80% of people to be immune and the vaccine only protects 50% of those vaccinated - which are probably fairly realistic figures - then the vaccine can't stop it from spreading. (Note that this is also likely higher than the herd immunity threshold from people actually catching the virus naturally, since that gives immunity to people more likely to spread it but there's no way to control who gets immunity from vaccinating everyone.) The general suspicion amongst experts seems to be that the current wave of vaccine candidates are probably not going to be effective enough to allow ending the control measures that have been put in place.