Think dolphins evolving the same fins and tail as sharks, despite having bones and needing to breathe air.
I will grant you that dolphins and sharks share the (main) dorsal fin, and I will also grant you that the pectoral fins of sharks and the flippers of dolphins are cases of convergent evolution.
But as far as tails are concerned, cetaceans differ from sharks, most fish, and ichthyosauria in that they have flukes (horizontal fins, like wings on a plane) while the others have caudal fins (vertical). Basically, ceteans generate thrust by moving their tail up and down, while fish (et al) generate thrust by moving their tail left and right.
In my view, nation states are largely the product of the whims of history. Nobody could look at a map of Europe in 1 CE and predict where all the borders will run in 2025 CE. In other timelines, Austria is part of Germany because the Habsburg never became as dominant.
You are correct that technically, the smaller the sovereign state, the more voters can affect their own affairs. If you are living alone on a sovereign island, your vote really counts! However, there are tradeoffs to consider. Coordination is difficult, and larger states often have a smaller overhead fraction, because maintaining a criminal code for 100M citizens is about as much work as maintaining it for 20M citizens.
And of course you can have layered federalism. If you are a citizen living in Frankfurt, you get to vote in municipal elections, state-wide elections, German federal elections and European elections. On each level, your vote is diluted more, and people from further away who speak strange dialects or weird languages have an influence in the matter, just like you have some influence in their matters. However, few people argue that Hesse or Frankfurt should secede from Germany.
I agree that the EU has a deficit of democracy, in that the rules are made by the governments of member states for the most part, and there is no direct democratic influence. But this is the doing of the nationalist faction. I also agree that some policy proposals put forward by the EU are horrible.