But yeah, other factors outweigh this significantly. If you grow up in an extremely poor area with limited resources, then having an IQ that's twice the national average is probably not going to help that much. Even in places with a working political system, things like economic class, your parents, plain luck, etc have a huge impact on your chances.
And heck, even then it's not guaranteed. People don't vote 100% rationally, and the politician who does well is often less the guy who knows most about the issues affecting the day/has a better academic pedigree and more the one average Joe can see themselves going out for a drink with.
Even then there's still a good risk of this potential high IQ politician having the 'wrong' political views (which would make them virtually unelectable), the media not taking them to them well (which could destroy their reputation) or people in general just not liking them for whatever petty reason.
As you say, merely making them smarter won't result in them ruling the world, and nor will improving every other characteristic/quality necessarily do the same.