Even if a AI president is in place, providing policy direction to maximize some agreeable set of end goals - the humans around the president would not understand the nuances, nor effectively able to / want to implement the policy given their own agendas. I feel that systems is bound to fail.
Now if only the AI president is able to do behind-close-door deals with politicians and special interests groups, some of the the policies might actually get implemented. But the end goals could shift pretty radically in that scenario.
I am having a hard time visualizing a scenario where an AP president would be effective / useful.
Maybe a human president could use an AI advisor to get data-driven arguments to support his/her policies.