Earlier quoted context omitted.
The issue with free movement of labor is that it only works out well across a region with standardized pay rates. Otherwise corporations will import labor from the low-cost zones and fire their high-cost local workers. This causes a lot of anger, see Brexit.
An outcome of free movement is flattening of income distribution across geography. Nowhere stays cheap, as wage inflation hits, and nowhere stays expensive, as employers move to cheaper places. Sure, cities will be wealthier than the regions, but ultimately a city in Romania and a city in sweden, infrastructure and education being also equalised through structural funds, should present equal opportunities.
Completely disregarding the language barriers, which are quite extensive so practically freedom of movement would be easy for corporations to use the benefits but not the wider population even if you neglect family ties.
These questions need to be answered and I don't think the educational elite has an answer without painting flowery pictures not too many might be inclined to believe.