Well, it works OK as long as the countries involved don’t get taken over by a demagogue, dictator, or whatever the Brexit movement was. In other words, rationality and cooperation go out the window. Which turns out to be a pretty common failure mode according to 21st century evidence.
Indeed, and it's a serious problem. There are really only two ways out of this mess and one is not at all like the other and both are roughly equally likely by my reckoning.
I believe the problem is that the premise is false. It works OK for a part of the population that feels comfortable with it. When you look closer at the root causes they are not immaterial and often boil down to people not wanting immigrants around them. If you are progressive you can just dismiss their outdated attitude - and this is what center- and left-wing politicians were doing for decades. Ignoring and ridiculing these folks caused the radical right to grow stronger in several European countries. Putin knows that and that's why he is sending more and more of them to Belarussian borders.