> education in politic/economics/&c

That doesn't magically make a person competent in other matters. On the contrary, many politicians with a background in economics or law show a frightening lack of insight in many other topics like environmental issues, information technology or science, whereas you will find plenty of experts within those fields (as well as economics and law) within the general populace.

The claim that elected politicians are somehow more competent than we are is a scary one. They are people just as we are. They have limitations just as we do. They specialize in various fields like they do, and just like the rest of us, that often means they don't really know that much about the stuff that is outside their own field.

Politicians in Western democracies are demonstrably not more thoughtful, deliberative, logical, rational, or intelligent than their average countrymen.

This. An advisory referendum is advisory. Constitutions use advisory refs for issues that are complicated and not suited for direct democracy. In the UK though, politicians were too coward to do their job and treated the referendum result as law.