Like any governance body, there are flaws...but it is a myth that it is an unelected un-democratic institution.
https://en.wikipedia.org/wiki/2019_European_Parliament_election
There are even parties within the system.
Nigel Farage and some of the other hucksters have tried to convince Brits that they are at the mercy of a faceless bureaucracy. But it isn't.
What galls Brexiters the most is that England doesn't get to dictate all the terms to the rest of Europe.
What it was designed to do was to create a unified system of regulations and rules for trade and commerce, so like the US, big business is right in there helping to write the rules.
It was also designed to create a single trading bloc of liberal democracies that would be able to withstand the insidious interference from Russia and the US. It has been very successful in doing this. There is no country that has had its actual sovereignty diminished or compromised by belonging to the EU...but many have had to drag themselves into the 21st century in order to meet higher standards for goods and services. 
For the Brits, it comes down to one thing and one thing alone.
In a post colonial world....after the decades when they have been forced to accept the subjects of their former colonies and now Commonwealth partners, Brits are drawing the liine at more brown people with cranky religions.
At the end of the day, this is only about one thing. Immigration. But if you ask many of the Brexiters, they believe they should be allowed freedom of travel and work and living in any country in Europe. Just don't want the same for foreigners coming into their country.
I have family both in England as well as Europe...it is a fascinating discussion taking place.