The EU have been showing signs of a dictatorship for years. Their Presidents are not elected by the people, and they allow little room for debate. Ursula von der Leyen has been voted in as the President of the European Commission, that's the most politically-powerful position in Europe. Yet in Germany she's seen as a failed Minister where she had only modest gains as Family Minister before making a balls-up of the Defence Minister role. She was in Bulgaria this week preaching EU values and refused to take journalist questions.
Christine Lagarde is President of the European Central Bank, yet she has dodgy financial controversies in her history (check her Wiki page for more details). Juncker, Tusk and Schulze have not been shy in being overly-confrontational with UK ideas, at best this is undiplomatic behaviour not befitting EU Presidents.
Something stinks up there in EU chiefland. What can EU members do about it?
People forget why David Cameron allowed a public referendum on Brexit: it's because he recognised this stink and requested EU work towards reforming some of their top-level processes so that they be more transparent to the public. This was arrogantly rejected by EU chiefs. Cameron's reaction by allowing the UK public to vote on EU membership was in theory a fair and rational thing to do, but he underestimated how fervent the pro-Remain crowd would react. We've thus had 3+ years of poisoned shouting rather than rational informed debate. It's been so poisonous that a lot of us are asking if it was worth even having the referendum in the first place. Better the devil you know and all that...
Brexit would force the EU to reform in ways that Cameron had suggested (more transparent), as the EU would not want to risk any other members pushing for their own Exits. That's the position of the left/liberal-minded person who supports Brexit.
No, he didn't. There is a lot wrong with the EU but none of what Cameron proposed to do (either in his "negotiations" beforehand or in the referendum) was designed to reform it for the better; that is why he lost, and why the moment it became clear he'd lost, he ran off.
The irony is that we actually probably are the best placed nation to reform the EU in the way you describe, even now - we have the oldest, most stable, most powerful and most aggressive legislature of the 28 states. A smart PM could have looked at the problems with the EU, recognized that the leadership will never try and fix them (and they won't, because they would lose out), and recognized that the way you deal with that is via the Parliamentary route (just as we did between 1660 and the mid 1800s).
If that hypothetical PM was able to build a movement that could win a genuine majority in the EU Parliament, everything you cite as a problem could then be fixed - the legitimacy that control of the Parliament would give would inevitably sweep away anything that stood in its path; it would become sovereign (as ours is).