Putting away the windup - you don't think that this:
'Decisions as important as Brexit should be taken by intelligent people on the back of extensive quantitative analysis and consideration of public opinion.'
almost perfectly describes our 'democracy'? We don't currently elect people (Corbyn aside most of them are rather intelligent) to not only take decisions for us, but to ensure that the process used to take those decisions involves as much rational, objective, quantitative analysis as possible? I think that's exactly what MPs do all the time, and it's what the public expects.
And the only way that Brexit was going to happen was to circumvent that process, in this case via a referendum. And surely there is an argument to be made that since our democracy works this way now, a decision as important as Brexit is precisely the sort of decision which should be taken this way and not one that should be exposed to a one off vote and all the flaws associated with that approach.
And I could turn your argument about criticism of the referendum really meaning that we don't like a process that results in an outcome we disagree with around. Are you really that happy to govern by referenda, or are you just happy that this one went your way?