There are independence tensions within European countries (eg. Spain/Basque, UK/Scotland).
You have to be a blind idealist to think this would work. There are going to be a lot of crisis scenarios for EU in the next few decades, refugees being the looming one EU failed to reach a consensus on and botched previously (that helped radicalise parts of it like Hungary and further alienated UK). The pending post COVID inflation/economic shock could also storm the Euro zone, Greece is still devastated from the "bailouts" in the financial crisis.
You are confusing independence from nationalism. They are very different things and you can have the first without the second.
Measures were not dictated by EU, each country decided it's own policy.
