What we do in hospitals and schools is employ experts to safeguard and prioritise the interests of patients and students. Those experts (unelected because patients and students don't all have the skills to judge who would be good at it) ultimately report to people who are elected to be accountable for all patients and all students. If they do their jobs badly, they are replaced.
So what would happen if you did ask the patients to run the hospital or students to run the school? What priorities would they have and what would be the consequences? Firstly I suspect that there would be a significant proportion who would understand the objectives of each institution and would immediately realise they needed help to make decision before they changed anything. But there would also be plenty of patients and students who wouldn't understand about the consequences of their decisions and would only learn those lessons the hard way. Their objectives would be short-term and probably naive. Self-interest would probably prevail. But the rules say the majority get their way. In hospitals and schools there might be fatalities and exam failures, but ultimately one might hope the patients and students would realise they need those experts.
But with Brexit, there's no second chance. No oops moment.
Tragically we have asked the British people to fly the plane and next Thursday they have to land it. If it crashes, all we can do is blame the idiots who asked them to fly it, and the passengers who ignored the pilot's advice and thought they knew better.
And if you need more advice, you must listen to this expert: Prof Michael Dougan an EU Law at Liverpool University