I doubt that the EU is falling apart, but if it ever does, then certainly more because of perceived issues rather than real ones. Although it was created democratically and by countless unanimous votes of its member states, the EU has always been an easy scapegoat for national politicians who did not do their own job right. In the UK, they quite obviously got the revenge for this behavior. (Remember, most MPs were and probably still are against the Brexit, and for good reasons, of course.)

The good news is that the vast majority of national politicians know fairly well how they abused the EU rhetorically and that their own countries would be crushed by global economic pressures if they left the EU. The UK and Germany are quite possibly the only countries who may be able to afford to leave the EU without major harm, and most smaller countries are aware of that.

But I agree that the perils of cheap populism and nationalism ought not be underestimated, and let's not forget that weakening Europe is in the current interest of Russia, the US in the eyes of the current Trump administration, and maybe even China. Anti-EU forces are strong, no doubt about that.

In the end, the current state of discussion is rather saddening anyway. The EU was primarily funded as a way to prevent Europe from being destroyed by inner conflicts again, which makes some sense after two devastating world wars that left Europe in ruins and killed millions of citizens. It's sad that this is sometimes forgotten and only emphasized by older politicians.