One could imagine lots of ways to have a unified planet without one centralized government. The EU is certainly one model you can achieve unification at large without "one huge government" as it consists of many smaller governments coming together.
Personally I don't really agree with your assessment of the EU as a form of that though. In this context I would include something like the EU when talking about larger governments (maybe that's not strictly correct, but it is what I had in mind with my original comment). There are of course lower levels in the EU (i.e. the individual countries) but that's also true for many countries with a central government and smaller regional authorities (e.g. London & Edinburgh).
"The EU is certainly one model you can achieve unification at large without one huge government as it consists of many smaller governments coming together."
That's not really what the EU is. The EU is a One Huge Government that has taken over some of the powers of the Less Huge Governments that Europe already has. It isn't a talking shop or forum for collaboration. It's a government which creates laws and enforces them. The fact that it doesn't control everything yet doesn't make it not a government, and the EU's core supporters are like ivolimmen - they want one world government and see the EU as a step towards it.