Your "Moreover, countries can leave at any time, as the UK has just done." sounds a bit odd in the context of this argument. "It's silly for countries to leave the EU on the grounds that it's not democratic, when it's obviously democratic because countries can leave the EU".
Yes, technically correct. What happened last time however was that the EP said "We want Juncker and we'll veto anyone else". There was a long staring contest and the EP eventually won. A veto isn't a technicality that you can approximate away - it's just as important as being able to propose laws.
The national leaders generally didn't like this, because they prefer the EU being more like a (huge, weird) deal negotiation table than something with direct representation. The national leaders are ultimately in charge, so this whole episode is mostly an unforeseen consequence of past treaties that they're willing to tolerate.
But hey look at EU over there
Moreover, countries can leave at any time, as the UK has just done. All round, seems to exceed your criteria.