> Passports for EU citizens aren't stamped anywhere in the EU. I live in Denmark. Would the USA know if I flew to the UK, then the USA?
This kind of question is a weird one to me. It's like "oh, marijuana prohibition hasn't worked so we should tax it and regulated it".
If you're breaking the law, there's sanctions. You may or may not get caught, and you may or may not be penalised, but that imperfection doesn't decide if it's valid or not. The jails in every country have murderers in them, but murder has been illegal since time immemorial. No-one proposes that we allow murder because with the prohibition we simply wind up with people in prison.
And there's a big difference between free movement of people versus a limited funnel of people. If it's still early enough, that could make the difference between something that is containable and something that is not, and it might make the difference between ICUs that can cope with the peak and being completely overwhelmed. (However, I think the horse has already bolted on this one.)