The obvious rebuttal to your first point is that Texas and California share a language. They also share quite a lot of culture. Whether a Texan is more like a Californian, than a German is like an Greek, I leave to the reader to decide.

There is one other thing. Identity is hard to impose. Most Americans of my acquaintance hold the US constitution to be a centrally important document. Otherwise they wouldn't argue so much about its exact meaning. There has been an attempt at a European constitution. It seems to have been a dismal failure. All the other arguments about border controls, the euro, farm subsidies and so on pale when compared to this. If you can't win hearts and minds, you can't win.

Though sometimes it appears you can achieve the appearance of winning through bureaucratic confusion.