Firstly, it seems to me that it could potentially poison his brand overseas. Everyone knows that Facebook can potentially exert a lot of influence in very subtle ways. How many countries would want most of their citizens under the potential influence of a company owned by the president of a potentially hostile country? It could cause Facebook to be banned in some countries (like it already is in China).
Secondly, it could be argued that the owner of Facebook already has more power than the US president, so it would be a step down. After all, Facebook has influence over more people than POTUS. And considering the subtle ways we can be manipulated by social media, it can surely be argued that he can influence people more directly and more powerfully than POTUS.
So it seems to me that becoming President gains him nothing but aggravation and stress, and stands to lose him valuable overseas business.