What non-EU treaty has the British public been allowed to directly vote on? All I see are devolution and territorial integrity referendums.
While I think direct democracy is something we could use more of, we are representative democracies and direct vote is highly unusual. There’s a point to be made that direct voting on complex issues might not express the will of the people, since most people will be uninformed and vote without full understanding. I mean, we are on a Brexit thread.
This sounds like the UK political system (or at least the spread of viable parties) is crap. It does not say anything about the EU, though, just about the UK.
In this regard the democratic deficit of the EU is pretty similar to that of the UK or any other member state for that matter. Should it change? Perhaps, but leaving the EU due to “democratic deficit” when the country leaving is perhaps less democratic in its structure (first past the post) is ironic. Or fallacious. Probably fallacious.
You say people vote national governments exclusively on national reasons. Well, people do have strange voting customs (certainly, stance towards EU integration is for me one of the major issues I would deny a party my vote for), but if a population is not taking into account the stance of a government regarding the international organization to which they belong, it doesn’t mean people don’t have a choice, it means people are ignoring it, due to stupidity or lack of information.
Tl,dr: there’s not so much a democratic deficit as a lack of voter interest.