I honestly have no idea how this would work mechanically; I'm talking about a point in the future where we are a fully multi-planetary species with governmental

I honestly have no idea how this would work mechanically; I'm talking about a point in the future where we are a fully multi-planetary species with governmental bodies across planets, so the level of tech that's assumed here is already reaching the level of magic. If we don't assume magical AI, machines are never better than humans at social decision-making so I can't see the President of Earth being a machine in this scenario. What machines are better at is information gathering and processing, which would allow them to synthesise minor political events happening in one corner of the world more effectively than any person and then present findings to a human to make decisions on. In other words it wouldn't be machines doing the governing, but they fulfil governmental roles in that they make increasing bureaucracy efficient enough that a body of humans could realistically govern at a global level. This isn't necessarily a good thing. China already has an incredible level of surveillance and info gathering ability within its borders and while their governmental structure allows them to be very effective and decisive with it, I don't think it's a good thing for corruptible humans to have that much power. Cue our magical AI.