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.