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'.