While true, the question should be: is each European nation/the EU collectively doing those restrictions sensibly, or poorly?

If done in a similar fashion as the US has chosen, i.e. due to incoherent populism, it would limit the number of competent e.g. Americas, Canadians, South Africans etc. from joining the European workforce.

If done in a sensible fashion, it would only exclude the would-be migrants from those (or other) countries who have shown a wanton disregard for democracy and other constitutionally required values.

Well they do depending on which country they are citizen of and where they are working.

The UK is considered non-EU so there would need to be a visa for a Brit working in the EU.

A nitpick here, but "visa" gets tossed around a lot. A visa is a document which allows you to request permission to enter a country for some purpose. To work in a country you need a work and/or residency permit. Even in the US, there are situations where you can work with a an expired visa, provided your other immigration documents are current. But if you leave, you need a new one. Similarly UK citizens can still work in some European countries without a visa, because there is no requirement for them to enter with one (but the officer at the border might still refuse entry).

You can be grandfathered in, but since this was about somebody returning to Europe, it likely doesn't apply to them

Again, depends on the country. Switzerland (which I appreciate is not in the EU) does not require visas for many "friendly" 3rd countries even if the person is coming to work.

https://www.sem.admin.ch/sem/en/home/publiservice/weisungen-...

Since the word used was "returning", that would mean that they go back to where they came from, where they are citizens.

this made me chuckle, considering

https://en.wikipedia.org/wiki/The_Odyssey_(2026_film)

Before returning from abroad, learn to string a bow.