And many countries already have relatively easy visa processes for skilled workers, which would be what these scientists, developers, etc are.
It'd involve spending money to sponsor research and clear a path for people to come over. Make it really easy.
If you're bringing these US Citizens into your country to get their skills, you want them working in jobs where they'll use their skills; or, you want them creating a startup where they can use those skills.
Requiring a job or getting an approved startup idea are both viable routes in the vast majority of countries in the EU, to my knowledge.
And, if memory serves, most people can get citizenship in those aforementioned countries in 5-6 years if they play correctly; and, many countries allow the US equivalent of a green card in a couple.
It's already pretty easy to move to Europe for knowledge workers.