Whether a government is too big or too small probably depends on perspective.
1500 years ago was the idea of a government for the entirety of the UK considered too much? Outside of a minority it’s seen as reasonable now.
If we ever colonize other planets then the perspective will probably change significantly. Entire planets being run by single governments, like countries are today, may well be considered normal.
So while some may scoff at the idea of there ever being a single government running the entirety of earth, history shows us that perspective is important. The UK (and many other countries, the US is a great recent example) used to be a collection of disparate tribes controlling small areas. Over time, as horizons broaden, communication and transportation improve, and cultures and languages merge, those small communities and areas have (for various reasons) consolidated into much larger entities, run by single governments.
In a generation or two the EU may end up as that, and a few generations later there may indeed be a single government elected for the entire world. Alternatively the EU may collapse as an entity having perhaps over extended itself or succumbed to a natural disaster or war, same with the US, China and other large countries, just as the Roman and British empires did.