History doesnt really teach us that at all. The political class 'manage' democracies in their own interests and they always have done. Brexit did not happen because the political class caved into some irresistible groundswell of public sentiment. A PRime Minister took a measured punt on a cynical electoral ploy which hugely backfired on him.
This isnt the political class caving in to mass sentiment. It is them misreading it and believing they can use it to their own short term gain. In other words, it was a mistake.