Such as how the British empire partitioned into the US, Canada, Australia.., or how China and Japan became distinct countries despite a common origin? Yes. A shared identity can support a larger country (the inverse can be seen in the breakup of Yugoslavia), but not without limit.
> I buy that smaller democracies could work better in many ways
It's not just about size. It's about the simple and intuitively obvious idea that it matters who chooses your rulers. I find it both fascinating and frightening that people have been so trained into ignoring their instincts (evolved through millions of years of inter-group competition, but now casually dismissed as "irrational"), that this basic notion now needs arguing.
[1] A small correction: I am not against the EU - the opposite, I am strongly in favor of it, for the simple pragmatic reasons that it safeguards peace among the member states, and because the relatively small European countries would otherwise be picked off individually by larger geopolitical rivals. What I am against is the expansion of EU law into areas of law and life that can be perfectly adequately addressed by individual states themselves.