The the office holder is where the power resides and where the decision is made -- they aren't a figurehead after the swearing-in, no matter what their role was in the campaign.

But, sure, depending on their background how "good" their head is, they certainly don't have to previously have been a chief executive to make a good president.

I'm mostly unaware of Jon Stewart's roles other than being on-camera / eye-candy, except for possibly some non-scripted interview questions (with him on either side). But, from the entertainment world, I think a directing experience probably does exist in the same "space" as chief executive.