For all the constant imminent doom of Europe predicted, though, public support for EU membership is actually quite high relative to historical values right now.
There is no alternative to a stronger and more cohesive Europe. The rise of Putin, Xi Jinping, Trump, and FAANG, is focusing a lot of minds - the only hope to not get trampled by these giants, is to stick together as Europeans.
What do you mean by that?
For a long time, these countries have reaped the benefits of Union policies without making a real contribution; they enjoyed economic solidarity (by being the largest recipients of European funds) and then refused it on social and humanitarian policies (like sharing refugees). This is unsustainable in the long run.
This is actually a great way to root out local corruption and to force companies to innovate, rather than lazily relying on guaranteed local contracts. It also enables them to compete over the entire EU market, on a level playing field. And it's doing wonders for your economies, which have grown quickly and consistently.