Instead of arguing whether this is possible or not, I will approach this as if it were possible. I would think this person would be pretty wishy-washy. I don't think he would be the best of both worlds... but more like in one of his own. He would have none of the definable traits in MBTI. If you look at it from a function perspective, and he is equal on all of them, he would be in the same boat. He would be balanced, but so much so that he may have a hard time making any choices, or change his mind frequently. His type could really be XXXX/unknown. Perhaps a 17th type? I suppose with proper control he would be able to blend well with any type, and be a jack of all trades of sorts... Accepted by all, but identifiable with none.
Of course, keeping a perfect balance on all traits at all times and it actually being (for the sake of argument) factually true... seems super human. Thats what I think anyways...