I absolutely agree on the matter of nation states. Because they have been the reality for longer than any living human being can remember we usually consider them to be the natural order of things.
However, on a historical scale nation states are a fairly recent concept. Before the 19th century allegiances for the most part were much more local on one hand and centred around religion (rather than concepts such as nationality) on the other hand.
Nation states helped with getting rid of feudalism and gradually ushering in modern democracy. So, historically they certainly were beneficial. In my opinion, they're increasingly and continually becoming obsolete, though.
That doesn't mean, however, that a supranational entity such as the EU necessarily is the right solution to each and every problem in the future. As much as nation states served a purpose in pre-globalisation times the EU was useful in the post-war, Cold War era but it remains to be seen if or in which ways it can continue to be useful in the future.
On the matter of Brexit it'd be pertinent to ask why a disintegration movement should stop at a national level. Why not further devolve power to for example the countries the UK is made up of or eminent city 'states' such as London?
I concur in that I think some aspects are probably still best dealt with at a unified supranational level (foreign policy, currency, removing trade barriers) while a lot more should be handled at a local level.