Thor Odinson isn't a super hero, either. He's the Norse god of thunder. Those are his everyday clothes and Thor isn't a code name. It's his read name.

Super heros have costumes. Fighting evil isn't enough to qualify. Lots of people, real or imaginary, fight evil. Super human abilities aren't enough, either. Batman has none, Green Arrow has none, but they are both super heroes. Why? Costume + fighting evil + use of code name.

Doc Savage is not a super hero. He may fight evil, but he doesn't qualify as one. Super heroes use code names ("Doc" is a nickname, not a code name like "Bronze Guy"), they also wear costumes. Doc wears quite normal clothing.
Everyone says he influenced super heroes. He did. So if he did, how can he also logically be a super hero? Also, he is not forgotten. Will Murray has written several new Doc Savage novels.