You're also eliminating one potential source of infected people leaving the country before symptoms show. Assuming prevalence is equal in the US and Europe, you gain exactly nothing.
(Op already said as much. Your answer reminds me of my Grandmother: "I know God doesn't exist, but it can't hurt to go to church.")
> Assuming prevalence is equal in the US and Europe, you gain exactly nothing.
That assumption is wrong, the prevalence will not be equal. One will be better off, one will be worse off. There is no scenario where the prevalence is going to be identical across such massive populations with such dramatically different cultures, population densities and healthcare systems. The US and various European nations will not act the same, they will not quarantine the same, death rates will vary, and so on. In fact, it'll vary considerably just within Europe, as we're already seeing.
It's better to separate accordingly, for both sides.
(Op already said as much. Your answer reminds me of my Grandmother: "I know God doesn't exist, but it can't hurt to go to church.")