The president of the US already does not really run the US, let alone the world. While they obviously have a lot of power and privilege, they are ultimately beholden to the capital owners of their country. For example, US is not supporting the genocide in Gaza because Biden is a Zionist. Rather, it's that his Zionism was mandatory for him being the president.
Besides the pedantry, Harris would become the interim president. I would love if it happened though. The scenario sounds hysterical.