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