I don't think he'd want the job, but he would do it were he asked and give it 110%. He's no nonsense, a facts-based decision maker, and he listens to people's issues and makes fair decisions if it's what you want to hear or not. He's also not too full of himself to admit when he's been wrong. He seeks out experts on matters outside of his experience and respects their opinions. He loves his country and looks to do right by those that entrust him with a job.
He would also probably be unfortunately remembered as a terrible president a la Jimmy Carter, as he'd likely trust a number of people he shouldn't to keep their word, he'd be too compromising for a lot of people, and I don't think people would like his "lack of personality" they'd get from his public persona. I think Hank would be a top-notch cabinet member though! I would totally support him for any of a number of different ones.