TLDR: no union without solidarity + solidarity is more than a lip service, it can cost you, so don't whine.
Given the notion that a country, and likewise a unions, stability ultimately depends on the sense of solidarity between its members (which are states, representatives and citizens), the EU is over. You can force it a bit to draw it out (others, like business, want the EU nevertheless), but eventually it will fall apart (like we are seeing in Belgium on the nation scale? not sure), or needs to adapt not-so-democratic means as a glue (for exampling the way Spain keeps hold on Basque and Catalonia).
So yes, it is up to us to have a union with solidarity throughout, or retreat to smaller units where that solidarity still exists. I doubt you'd find many a, e.g., Frenchman who would seriously consider giving up on France as unified state in favour of splitting it up again into smaller regions, and this is because there is this mutual solidarity encompassing most French, who know that 'somehow' they belong together. This sense of solidarity has existed in the 80s and 90s in large parts of then-Europe (although maybe never so much in the UK), but appears entirely lost now. Most have long retracted to the nation level, when evaluating who they share an interest with.
So if there is no common ground for Europeans, leave it be. I really dislike that, but if its like that, well bye.
Another thing:
It would be better to build the union on a continuous strive for solidarity, instead of just allowing "i wanna be in but no play along" mentality that most countries display at the moment. It should be really easy to drop out of the EU, and very hard to (re-)enter. It should for example be enough to drop out by not showing enough positive engagement for furthering integration alone. Then the union would certainly be much smaller or not exist at all, but at least it would be certain that all members, if any, would actually be there out of shared interest.
Anyone else can form a free trade zone, if that's what they prefer.