I believe there’s a fault underneath your reasoning, that is how comfortable you are in calling this “democracy”.
I rather believe that what happened is a different dynamics, closer to a “hustle” perhaps. What happened is that a bunch of very smart people have manipulated the demographic majority of the population into voting “something” that served their interests. The real winners are the manipulators, not the leave movement. The facade is of perfect democracy.
E.g. the Tories needed to make Cameron into a loser to get another Tory to lead the next government, otherwise the natural dynamics of unsatisfied people is to switch vote. That is also why Cameron was among the leaders of the remain movement. If remain won, Cameron would have been triumphant and stuck around. If leave won, Johnson would have naturally inherit the throne, that is what will happen soon. It’s just by chance that the Labour party was in this shambles, it made the job even easier.
So, what’s the demographic majority of people that is the easiest to manipulate today? Clearly the elderly and/or uneducated. Never before these were in such large number, and never before manipulating them was this worth investing into. What do these people respond to? Fear(s) and money (expressed as multiples of nurses’ salaries). Easy peasy. Not a new strategy by the way, Berlusconi did the same in Italy in the 1990’s, with the advantage of controlling three national televisions.
So, should we be really celebrating democracy? Yes, but this is not democracy, this is exploitation of a corrupted dynamics. The “wisdom of the crowd” only works when the crowd participates without being influenced. In the classic Francis Galton’s anecdote, people guessed the weight of an ox at a fair. There was no personal engagement whatsoever in the guess, their lives did not depend on the guess being right or wrong, there were no media promoting one weight or another, there was no information whatsoever about the ox, truthful or false, people just needed to go and see it for themselves, and it was — after all- a very simple exercise.
So, what now? I don’t know. But, formally, the decision definitely was democratic, nothing we can do about it. Hopefully, we can manipulate democracy back to do create such opposition to the completion of the process that it won’t happen.