The thing is now with polling firms we now have accurate (well, somewhat accurate) reflections on how the public feels anyway. Isn't a plebiscite just a glorified poll?
There is big difference between expressing an opinion to a pollster and actually voting on it. After all most people do a bit of thinking before they vote and some take it quite seriously.
Besides if you have a political culture where going against the result of a plebiscite is unthinkable the difference between a referendum and a plebiscite becomes a trivial technicality. So it is a matter of establishing such a norm. But of course I am biased by coming from a country where the difference between "real" referendums and "consultative referendums" (=plebiscites) has never been considered anything but a trivial legal detail. Still, this is a norm that can be established over time.