The EU in its current incarnation as a centralised, geographically-defined bloc could be considered a relic of colonial, pre-globalization times (as much as nation states are a remnant of pre-industrial, pre-Information Age times).
In order to be able to address the issues of the 21st century we need a much more decentralised structure, more devolution of government to the local level and more cooperation between these decentralised entities.
Large cities in different countries and their respective populations often have much more in common than people from rural regions have in common with these city dwellers (as evidenced by Brexit). Yet through arbitrary national borders they're simply lumped together. The same applies to border regions. Why shouldn't companies and other organisations from different countries be able to work closer together more easily?
Finally, why should organisations such as the EU be defined in terms of geography instead of in terms of shared values? As of now, Canada for instance would be a much better fit to the EU economically and in terms of values than some of the Eastern European member states.
There are a few interesting articles about this subject and 'neo-medieval' overlapping authorities and multiple identities as a possible outcome:
https://www.newscientist.com/article/mg22329850-600-end-of-n...
https://stratechery.com/2016/the-brexit-possibility/
https://fieldnotes.mike-walsh.com/brexit-and-the-rise-of-the...