The public is never ever ever wrong. It is infallible. That's the starting point of democracy. The instant you stray from that, you're fucked. You can't say "the public are stupid and can't be trusted to decide on Brexit" and also "the public are smart and chose me as a representative to tell you how stupid they are".
Disagree.
The starting point for democracy is "One man, one vote" (or woman these days - political correctness gone mad, I tells ya).
So the premise is that everyone has a right to an opinion (true) and that everyone's opinion is equally valid (false - obviously false).
I shouldn't need to labour this point but if you're the sort of person who, say, thinks that were the earth a ball then the oceans would go flying off into space like water off a rapidly spinning tennis ball then your opinion about the shape of the earth is not as valid as someone who has a degree in physics and understands a bit about angular velocity.
People have different experience and knowledge. Of course everyone's opinion doesn't (or shouldn't) carry equal weight.
When it comes to a General Election then I'd suggest there's no "right" answer. Would I have preferred Corbyn to Johnson or Hillary Clinton to Trump? Probably, but in neither case was it clear that either of them were particularly good options. Increasingly it feels like we're choosing the "least bad" option.
When it comes to individual issues though...FFS don't ask "the people". We shouldn't decide to leave the EU because of a vague feeling that we are "British". I'd suggest we can be British and be in the EU anyway, the French certainly don't seem to have an identity crisis in terms of being French and they're in the EU. Nor do younger people in the UK. And, for balance, we shouldn't stay in the EU because some people think the sky will fall in.
The decision about this should be made based on careful analysis of the benefits and drawbacks of being in or out of the EU, not because John in Scunthorpe doesn't like the "bloody Frogs". You're right, it's not the electorate's fault they were asked, Cameron's at fault for that. He gambled on the Scottish Referendum, won that and went double or quits on this one. The dick.
I see you brought up sovereignty. To be honest, that was an argument that briefly swayed me. But then I realised something - we are sovereign. Any power we have ceded to the EU we have chosen to do so and we can take back if we choose to. How did we start the process of leaving the EU? Who did we have to go to war with? No-one, we just had to write a letter. The process of leaving is complicated but we didn't have to go to war because we are sovereign, being in the EU wasn't imposed on us. We chose to join, we can choose to leave. And we have. Is it the right decision? Time will tell. But if it is then it wasn't made for the right reasons and it wasn't made by the right people. People who know what they're talking about should be making these decisions. They might still bugger it up of course just like a doctor can misdiagnose people, but they've got a better chance of getting it right than hair-dressers.