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That's the double edged sword, not for the new arrivals, but those who already have EU citizenships can move anywhere. They don't do it much yet, except to relocate in another one of the country with a generously broken system of social benefits and/or currently more opportunities, but in any case they absolutely can anywhere. The specific piece of paper they acquired is irrelevant, especially since the whole ideology of the EU in the foreseeable future is to standardize Europe and turn all the countries into "regions" of the EU. Countries who rave about having no immigrants are as royally fucked long term as anybody else, as long as they stay in the EU, are not so poor and underdevelopped that nobody would ever want to go there.
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