From "across the pond", I'll be the first to admit that my understanding of the EU is rudimentary, but I always thought that it was a simple economic treaty/conglomerate, creating a loose combined economy to strengthen the economies of the individual nations and to make trade easier and more seamless. I also thought that it had nothing to do with governance, laws, or policies in any way shape or form that had nothing to do with economics.
How close am I?
Close enough, however that's not the whole story.
Where what you describe was the original set-up of the EEC (European Economic Community) founded in 1957, it has progressed into what we today call the EU. This Union indeed passes laws that are valid EU-wide.
BUT !!! ........................
The popular narrative (propagated by the disenchanted) bloats the three main bodies of the EU (EU parliament, EU commission and EU council) into something that they (singly or as a whole)
are not, namely a foreign government, elected by nobody and waltzing all over the sovereignty of individual member states and their nations.
Because, to sum up in a general manner, there's nothing that the EU can do that does not meet the approval of ALL member states.
The whole thing is a complicated construction and to describe it all would explode the thread here. But just as an example, an important piece of criteria for being able to join is that the applicant country does not practice the death penalty (has abolished it) and convenes to the basic tenets of human rights that all members have agreed to adhere to.
Another pet peeve that the UK Brexiteers have exploited is the freedom of movement, both of goods and people within the EU. Where goods are concerned, those were hardly the issue, but where people come up, this meant that Spain (where I live) could not say "we want to control how many Brits live here" and the UK, of course, could not say the same wrt Spaniards. Applies to all other EU countries as well, naturally.
Everything peaked in the general xenophobia (not just a British phenomenon) against letting in refugees from war zones and, not to understate that issue, economic migrants from the poverty world outside the EU.
Well, one can see how mighty the all powerful EU was on that question in superimposing large numbers of refugees/migrants onto any given EU country. Exactly zilch in that every country decided for itself (as it could) with most saying "no thanks".
What is swept under the carpet by the malcontented is that the EU is not the faceless governing body of power that they like to make it out as being. It's everybody.
And if everybody doesn't agree on the important issues (unanimously), nothing will happen (nor can it).
Bit of an overly simplistic summary, no doubt, but that's the gist of it.
What London doesn't appear to be getting to this very day (IMO extreme cognitive dissonance born from some still existing affliction of empire nostalgia) is that it takes just one (1) EU member state to say that they don't agree with one condition of the negotiated Brexit (say London insists on
no freedom of movement of people) and pow". Hard Brexit.