The figure below shows that if you do let “hard working people from other countries” move around a continent, then you do create unequal societies, at least in terms of GDP Per Capita growth which has a close correlation with the trend in living standards over time.
You’ll also see that those countries that have had the fastest rate of growth of population (examples UK, France Sweden) have had lower rates of GDP Per Capita growth than the countries whose populations have grown slower (eg. Latvia, Lithuania, Bulgaria).
You might say well that’s great because the GDP Per Capita is growing fastest in those “poorer” countries but you need to bear in mind they are starting from a much lower base:
Actual GDP Per Capita in France, Sweden and UK is around $48,000, opposed to an average of $29,000 in Latvia, Lithuania & Bulgaria.
It’s a matter of opinion I suppose whether you see movement of workers having this effect as a "good thing". To be in favour of it you have to accept that workers’ wages in the receiving countries will stagnate (along with their living standard), societies in the countries of origin will be stripped of workers (and continuity) and that therefore Gross GDP in the countries of origin will also stagnate.
Surely this creates the “unequal societies” you say you don’t desire?
It used to be that “the Left” celebrated Unions associated with nationalised industries and demonised anyone who crossed picket lines to undermine wages. But now it seems that “the Left” support the mass immigration of workers into a country who undermine wages and any indigenous people who oppose this are called racists. Many working people who voted Brexit have probably just seen the manifestation of this in their daily lives and decided they just don’t want it any more.
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