Well, in most countries here so far the democracy works through elected parties. So sure you can have your vote but what follows is determined by the parties which you voted for.
We can only try and see what happens but direct people voting in referenda has a strong immediate feedback response which does not take into account anything that is actually happening as most people only hear what they read only on their favorite channels online (which can be 100% fake). It is a snapshot of the now: as has been shown after that many Brits would have not voted brexit if they were fully aware of all the (mis)information.
This has nothing to do with calling people stupid or ignorant; it has to do with some powers that be being very clever getting information out people act on and the EU rulers, so far as incredibly bad at this. They seem to be incapable of explaining long term benefits or what is happening at all to all the populous. This is a big problem. But even if it would be solved; the channels to reach are vast and diversified so if you just ask people to respond immediately, they will and you will get a very skewed look.
And yes, agreed, there is a lot wrong but a lot of it is also miscommunication or actually no communication from the German and Brussels towers. That is wrong but asking 'Joe on the street' about immigration, I can predict their answers based on who you ask, even if this is not in their best interest.
I cannot see how this will win anything; it will surely break up the EU, which could be good in some universe, but yeah, it was not great before the EU (to say it mildly) for many member states, so what data do we have things would improve? People have never experienced this prosperity: I cannot see, unless directly asked in a moment of angry 'took ma jubbbbs', how anyone besides Germany or France would benefit from leaving and they do not want to.