A curious thing about The Librarian is that he is a genius but not an intellectual. He knows everything, but he never seems to think very much about anything; his vast knowledge is merely the tools-and-weapons kit of a detective/action hero. That’s what he is. He’s not big or macho, but detective stuff and action hero stuff are what he does. That’s all he has to be in the context of the plots he’s put in.
What fictional heroes are also intellectuals, in a way that is essential to their characters? The first that comes to mind is Elric of Melnibone.
In the comics, I would point to many characters written by Dennis O’Neil, Steve Englehart and Steve Gerber. The Question, the Beast, Dr. Strange and the third Foolkiller all seem to take the broader view.
I suppose it goes back to Mycroft Holmes, who could solve mysteries without his brother Sherlock going every which way gathering clues. Poe’s Dupin didn’t seem to attached to the physical world, either, and solved mysteries by his “ratiocination,” based on only what he could glean from the most common sources.
Smart, even intellectual, detectives are a dime a dozen. The SMART ones are those that can solve a mystery from an armchair at their favorite club.
OTOH, Sherlock Holmes held back evidence until the final reveal, and I assume the rest do, too.
Wolfe wouldn’t leave his brownstone for the purpose of solving a case. He would leave if given enough incentive…such as an orchid show, or if someone flattered him enough to cook a meal (Fritz was an excellent cook, but Wolfe was an even better one). Wolfe was ready to enlist in WWII, apparently as a common soldier, but Archie (who was an officer) manage to persuade him that the US had enough men who could shoot a rifle, but that Wolfe was a genius who shouldn’t be wasted as cannon fodder. Wolfe also visited a restaurant on a regular basis. However, for the most part, Wolfe was very happy with his home and didn’t set foot outside of it.
Batman is traditionally portrayed as being very intelligent. Not only is he fabulously rich, but he’s an inventor, and makes most (if not all) of his special gadgets. It’s true that he’s very athletic, but all of his strength and agility would be for nothing if he didn’t have his smarts, as well.