Even though Gates has as much money as he does, he might be small when compared with the global banking/money system. In that case, he might desire a formal global government just to keep himself from losing value, because the current banking system is raping him just like they are raping almost everyone else.
There is the other scenario, however. Gates might be trying to promote a global government simply in a bid for the banking system to take over the world formally. In this case he would be working for and with the banking/money system to further rape everyone else.
Personally, I think Gates is moving in the direction of the former rather than the latter. I think Gates, although he doesn't want to harm his own value, is from the old school where people had to use their ingenuity and sweat to build an empire. I think he is fighting the big banking system like we all are (remember, we are Bitcoin?), and this is the way he is trying to conquer the corrupt banking system.
I also happen to think that a formal world government isn't the answer... at least not if it is built like any that we currently have. We need a government system that is trustless, like the Bitcoin money system would be if it were implemented worldwide. What would such a world government system look like? Good question. Lots of thought and experience would have to go into making a world government of this kind.
It would need to be based on freedom for everyone, as long as there was no harm done to another, or damage done to another's property.
