A lot of times we like to put our literary comparisons at a super high level, when there's really no evidence to do so.  Is Conan a 15th or 20th level equivalent?  Why?  I'm trying to remember (I'll admit it's been a long while), but I think some of the toughest fights he's had were against a stegosaurus (which he had to poison to beat because he couldn't go toe to toe with it), and a giant ape that just about killed him (I want to say there were chains or something involved there).  Most everything he's fought would be the equivalent of CR 1/2 or 1/4 creatures.
If you look at the evidence and do the best comparison you can, most of our literary heroes would be no higher than level 10 or so.  I remember an article in Dragon way back when that had Gandalf as a 5th level wizard lol.  But really, what's wrong with that?  Back when levels had names, a 4th level fighter was a "hero".  To put it into context, a 4th level PC can go toe to toe with a brown bear.  How many people do you know can do that?  That's definitely what I'd call a "hero'.