The problem with a referendum and abstract propositions is that people all put something different behind the Brexit vote and it was then impossible to reconcile all the positions (plus all the empty promises like the 350m for the NHS). Brexit became something very different than what was originally sold and some people asked for a second referendum to clarify the situation now that things were getting clearer. This act can be criticized or misunderstood, but I don't think anyone can argue that Brexit is a very different animal 4 years later (the unicorn honestly looks more like a donkey up close).
Brexit has shown that the disconnection between the political class and the people had nothing to do with the EU. Dominic Cumming refused to quit despite being caught in clear breach of the lockdown is the perfect example of it.
The EU parliament is elected directly by the voters, and representative are nominated by governments that are also elected. The US has a completely different electoral system, where (like in the UK), candidates with fewer national votes can become leaders (I find these systems undemocratic, a voice is a voice, its geographical location should not matter).