How old is the EU? Already, after only a few years, the erosion of sovereignty of the individual countries is well along. I think it proves the point more than refutes it.
About 50. Nations have chosen to delegate some parts of their running certainly - more so than the US states in some areas, less so in most others.
Any answer to the first point? This debate is immaterial since in countries that people actually want to leave: a. their own government won't let them leave and b. our governments won't let them come.
The question I suppose is, can we find a way to reduce our borders without creating a world government, since that is clearly a bad thing? I believe we can, will and should.