In fact, I would, based on experience and some of the management training I have had, that being smart in an intellectual sense is less important than being smart in an EQ, good with people sense. A good leader, including a POTUS, should be able to pull together a team that has the intellectual smarts. They should listen to that team and work with that team.
The management philosophy we use at work is called the Ideal Team Player and that's really what is needed here. In the Ideal Team Player, one of the three core factors is being humble in the sense of playing as part of the team and not making it all about yourself. Trump's big failing is not being stupid intellectually, but it is his self-aggrandization and attempts to make everything about him. He can't hold together a good team because he keeps falling out with people and putting down even ones who are otherwise on his side. The other factors are being Hungry, which Trump has in spades, and being Smart in a people sense, not an intellectual sense. He seems to have some of that but not always in a good way. He is more someone who manipulates and uses people than works cooperatively with them.
So, if POTUS needs to be an "Ideal Team Player", he is not really suited to the job.