I guess at this point our issue is that the EU represents a great many different forms of international integration, from economic, to political, covering immigration, economic policy, monetary policy, policing, civil rights, food policy etc etc
The EU is assumed so many responsibilities over time that it’s difficult to talk about the EU as whole in a meaningful sense. You need to break down each aspect of integration that’s been built around it, as assess each policy on its own merits. When you start doing that, it quickly becomes apparent that some aspects of the EU work incredibly well, but other aspects have failed, sometimes catastrophically.
Personally I think the EU has been a rather grand, if lumpy, success so far, and I’m keen to see it continue growing. With it the merging of national identities across the EU into single European identity, with many nuanced sub-cultures.
> A trade and customs union with relatively free movement (but not fully) would be 'better' than the EU
On specific point. The EU has got a lot of flak in the UK for freedom of movement, usually focused on the stereotypical “Polish plumber”. It worth mentioning this was a self-inflicted pain by the UK. The EU gave all existing countries the right to limit immigration from the new joined eastern states, with 5 year ramp up period toward full freedom of movement. The UK opt-ed out, and decided for full freedom of movement from day 0, most other EU countries limited freedom of movement to prevent large economic migration. So all the limits on immigration the EU supposedly prevented the UK from implementing, were an completely legal option for the UK, it deliberately decided not to exercise them. Further proof that the EU has never prevented the UK from reducing immigration, is the fact that net immigration has fallen since Brexit.