I've said before in other comments that this wouldn't just take over from your geographical citizenship, but would be a sort-of competition to it. Competition benefits the consumers, because both sides try to create a better value proposition. Right now there is no competition to your governance other than potentially voting for someone else or moving. If we created a global body that isn't just some black-box bureaucratic system, but a 100% open, transparent, run by the citizens system, that could help put some real pressure on international politics.
Here's just a few Wikipedia links that connect to everything I've written in my comments so far. There's more than these, but I'm still working through them:
- https://en.wikipedia.org/wiki/Global_citizenship
- https://en.wikipedia.org/wiki/Democratic_mundialization
Maybe you could illustrate this idea with a few fictional scenarios. For example, let's say Citizens A and B are a law-abiding family in Germany, and the government there has just seized their children because they're Christian and they homeschool. Clear violation of the UN declaration of human rights. What does your online government do to help these citizens?
I've revised the term to not mean "government", that's just what term I first used. Think more of like a world citizenship, or NGO, or union fighting for collective rights.