"It is increasingly clear that we need a supranational organization in Europe which IS a democratic government."
I don't think that's clear at all.
One could very much make the argument that it doesn't need 'governance' it needs 'coordination' which are very different things.
I feel the vast majority of the most important things could be achieved mostly by treaty and that everyone could 'have their cake and eat it' which is to say have fully sovereign states and work together.
I think there's quite a lot of a) ideology in the US of Europe b) it's the natural 'power creep' of any institution and c) the business class love to be able to 'skip democracy' and so do the 'socialist' types - both of whom kind of work in a weird kind of tolerance of one another, with I think the business class mostly in charge.
In particular, the hugely vague mandates on 'Human Rights' are the biggest coup, though the least obvious. They basically give a 'carte blanche' to the EU courts to rule as they see fit, interpreting some basic, bland text to mean whatever they want it to mean.
Since the EU courts often decide on their own jurisdiction ... it results in a huge concentration of legal power.
It's a Judicial takeover.
Something similar happened in Canada - not exactly on purpose - but when Trudeau Sr. introduced a new Constitution into Canada in the early 1980's - it was a 'nice modern document' but obviously vague. Since then, the Supreme Court of Canada has struck down innumerable old laws, new laws, they do it all the time, they even 'change their minds' on things like terminal care and suicide. Because of the vague wording, 'the world's top legal scholars and lawyers' have no clue what legislation is legal or not, it's just a matter of what our 'Tribal Council of Unelected Elders' decide to do. It's resulted in 'Law by Judicial Fiat' for a wide array of issues - all of the most important ones (identity, rights, marriage, abortion). Canadians, elected officials, politicians, the Prime Minister have little say in the matter ... except for this weird clause someone can effect which basically says a 'law is not bound by the constitution' - which is crazy in of itself.
The 'Human Rights' mandates of the EU are controversial for this reason: obviously, they are humane and positive i.e. a 'good thing' - but many people oppose them on the legal problems the effectively create. These people are easily lambasted in the press as 'anti human rights' which is of course completely wrong.
Europeans are quite smart, the lack of understanding of these things is really quite bothersome. People just seem to be happy to do whatever the elite tell them to do.