Basically, no. What you're asking for is what the EU has tried to do somewhat: become a confederation. It doesn't work. The USA tried it back in the 1700s and it was a disaster. The country couldn't defend itself, have any kind of central banking and currency, or any consistent policy. It was replaced in 12 years with the more centralized federal system that exists now.
The EU was created because the European nations wanted to be a powerful continent-sized political entity that could rival the US, and have the same benefits and power on the world stage. But there are costs to this: you need much greater centralization. Arguably, the US doesn't have enough centralization and this is causing many of its internal problems now.
Basically, if you want to be a world power, you can't just be a bunch of small, disparate countries in a loose trade confederation. You need more centralization of power, and the problems that come with that. If you don't want that, you need to just be happy with being a bunch of separate, sovereign nations with different currencies and trade barriers between them all. Pick one.
From my perspective, the EU's problems you see are because it won't just commit to a centralized system and eliminating national sovereignty, and it's trying to have it both ways.
> The EU was created because the European nations wanted to be a powerful continent-sized political entity
It was created as a trading bloc, literally the European Economic Area. That project later got hijacked by federalists who wanted to do what you say, but they never had agreement on that from the actual citizens. That's one reason the UK left.
> Arguably, the US doesn't have enough centralization and this is causing many of its internal problems now.
Arguably the US's internal problems come from too much centralization, hence why Americans famously loathe Congress but like their own Congressman/woman.
Yep but it's even more insane than that. The laws don't even come from elected people at all!
I'm all for European trade, but I felt I had to vote Brexit because obviously the goal of any political system should be to maximise the political power of individuals and local communities. The more you centralise and expand power over larger geographical areas the less tolerant of regional political difference your political system must become. This become obvious when we talk about a country like Turkey potentially joining the EU.
That said, I hate the UK government with a passion and they are arguably even worse when it comes to surveillance, but at least we can vote them out.