No. It's not a small price. Ask the board members from the US how much friction you always end up with when the federal government overrules state decisions and legislation. Here we're not talking about states that are only a couple of centuries old at best, but countries, many of which have been self governing for a millennia or more. But that is sort of besides the point.
Back when it was still the EC (the predecessor of the EU). Brussels was something too far away, with a commission that worked more like a board of directors, all of it's members being appointed, not elected. The European parliament has always been a joke. Back when I was still living there, it was a meme, that politicians who fell from grace in their home countries for this and that scandal would get the "golden handshake". Which was sending them to the European Parliament where they would spend all their time lining their pockets with unbelievable salaries and tax benefits. Out of sight, out of mind, not doing too much damage anymore in their country of origin. Which means, the real power is the commission.
EU was the move to centralize legislative power in Brussels, gradually turning national parliaments into something that is just a token gesture while all decision making should be done in Brussels, overriding any national legislation the member countries. I.e. effectively turning member countries into vassals of a powerful Brussels, which as mentioned before is not ruled by an elected body. It makes it too easy for large and powerful corporations, banks, other interest groups etc. to assert themselves, because there is only one point they need to convince if they want local laws changed to suit their needs. Don't like the minimum wages in country x, y and z? No worries, tell your lobbyists in Brussels to "get it fixed" and local law making bodies can do nothing.
So no, I don't think the EU is beneficial to Europeans. It's predecessor organization was, because it was a trade block, benefitting the member countries. The current project is just a power grab by the eurocrats in Brussels, wanting a strong, centralized power in a new "super state", doing away with the member countries sovereignty.
So yeah, as far as I'm concerned, the EU can rot and burn and I'll happily watch the flames while sipping aforementioned Cognac, pondering the folly of man who just can't seem to learn anything from history. The bigger they become, the harder they fall. I would like to invite you to the anarchists club, but there is no organization you can join, too disorganized 😝