What I see people (Europeans) lamenting is how undemocratic the EU is. As much as I think von der Leyen should be imprisoned, the issue is not the people in the government, but the institution itself. The Commission and the Council are the ones pushing these things, every time.
The people in government are bad, and there's no reason whatsoever to think that'll improve amy time soon: what prevents bad people from doing bad things is the regulatory apparatus of checks and balances, which the EU very much lacks (in parts, granted). Worse, it has introduced US style corruption (or "lobbying") into countries that historically lacked it.
If Chat Control 2.0 passes, given the general direction this would be showing, I'd very much understand people wanting to exit from the EU and cut the amount of undemocratic bullshit they have to contend with.
But to return to your point, when something people strongly reject happens in their country, they do, rightfully, advocate for the dissolution of that government. Much harder to do with unelected bureaucrats sheltering in another country.
The Euroskeptics want to go about this backwards. They correctly see the anti-democratic nature of the current EU structure and conclude that this is the only way European integration could happen, ergo we should not integrate Europe. The problem with this is that, even as 27 individual sovereigns, the former EU member states would still need to form agreements with one another and with other countries. Except this negotiation process is completely outside the democratic process even more than the EU currently is.
The underlying problem is that democracies do not stack or sum. Two democracies negotiating with one another become a dictatorship of whoever is doing the negotiating. The only way to preserve democracy is to give the people of both countries equal control over the matters assigned to the whole. The people must rule as one or they cease to rule at all.
The EU is handicapped by its very diversity on this. Imagine the situation where the EU is integrated, and the government wants to pass Chat Control 2.0, or some equally unsavoury measure. Imagine that some people or orgs manage to whip up the people of the Netherlands into protesting in the streets against it: it's extremely unlikely that Poles or Spaniards would be able to build a protest movement on top of that, if they were even aware of it, because of language and national sentiment ("it's just some people over there being angry about whatever, and mainstream media says there's nothing to see there, or that they're evil terrorists, and I don't understand their funny language enough to check").
There are some promising moves towards a EU-wide party in Mera25 for example (if I understand it correctly), but it's ultimately a party for English-speaking, basically well-off, educated, currently left-leaning, young people, which is nothing that one can build a deep movement on.
?! Yes. Well, to some of us maybe not yet chat control given some proper well conceived legislation. But age verification, yes, may be one of the reasons to ask for dissolution.