As someone born in a desirable place with freedom of movement, it's difficult for me to speak to those barriers from an informed perspective. It's very complicated. To what extent is progress about improving all places, and to what extent is it about enabling people to move to the good ones? If it is all about enabling movement, then having individual nationalities really gets in the way. Also, cultures that cannot co-exist with others in close proximity also get in the way. There's an interesting kind of phenomenon where the people that seek a place for one reason change it into another. Personally, I am ok with that. It's what I see around me here in the US, and it seems to be a good thing. However, the US is pretty unusual in that respect. We have a short history, a lot of resources, and a powerful Federal government. Ultimately, what I hope we see, is a world with freedom of movement, but places with all sorts of cultural and economic experimentation, that we are free to move into or out of. I really don't know if Brexit is a move towards or away from that.
When talking about the EU barriers in particular, I'm too young to remember anything else. The only big change I remember was the Euro being introduced, which only made buying stuff a bit easier on holidays. But I do know a bunch of people that have benefitted greatly from those removed barriers. Especially at a university you meet so many people from other EU countries or people who have lived abroad for a while that Europe might as well be a federation. Personally, I think having great mobility will inevitably lead to great places. How great that place is depends on where its drawing it's people from. I grew up in the capital of a rural-ish provence, where not infrequently the local newspapers lamented that capital for draining the countryside of people and knowledge. But at the same time, there are articles out there talking about the mobility of people from those peripheral provinces of the Netherlands towards the big cities like Amsterdam and Rotterdam, which is a move I did myself last year. And there are people leaving those places to move to Berlin or London. Each successive place can be seen as contributing more to progress. There's a reason the very first thing urban geographers are taught is Christaller's Central Place Theory - while it is outdated, the idea of a hierarchy of cities is still relevant. The degree to which culture plays a role in this can definitely be argued over, but as someone living in a culturally rich and very dense country I feel like there is always room for cultural diversification and experimentation.