I don't think "One huge government" was claimed. The claim was "one planet", which I think more means people should be unified more than we currently are.
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.
Perhaps I did misunderstand, I was certainly interpreting it as a desire for concrete change in the political structures of how the world is run rather than a shift in attitudes amongst the people of the world. I'm definitely not opposed to less conflict in the world!
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).
"One planet" is a slogan without meaning because we're already one planet, so the reader is forced to interpret it in the most likely way it was meant - as one world government. The mention of being super left wing, and the context of the EU makes that interpretation far more likely.
"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.
The fact that you derive “one huge government” from “one planet” probably speaks more to your biases than anything else.
There are plenty of models that would allow for a small level of administration globally and local governmental control that is still considerably better than what we have today.
For what it's worth, the UN could be reformed into such a government. The problem is only that billions of people live in dictatorships of one kind or another, and then the world would suffer under the collective rule of the dictatorships.
One world government would be so ineffective, totalitarian and corrupt that it would be in a state of either constant uprising or permanent heavy handed suppression. It would definitely not be "peaceful" except in the sense that an effective police state is "peaceful" because anyone who suffers from it is crushed, before they even get to the point of being able to disrupt the peace.
How would an ineffective, totalitarian and corrupt goverment manage to supplant all the existing ones? I think that if a world government manages to form, it cannot be any of those things. To unite all the peoples of Earth it has to be efficient, democratic, and just.
By exploiting people with views like yours, and by hiding the truth about it's own nature? Look at the EU for an example of how to do this. The hard core remainers are all convinced anyone who doesn't like the EU is brainwashed, racist, stupid or all three but they struggle to keep up in a debate involving the details of what the EU really is and how it works. That's what converted (deconverted?) me: realising at the start that my pro-EU position was based on the sort of wishful thinking your comment implies. It's all about cooperation and world peace, right? Then I listened to the Brexit campaigners and discovered that I had no idea what was really going on in Brussels. It was very far from the friendly face.
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.