Yes, absolutely, the problem with a Superhero though is that they make the Doctor largely redundant in his own world. Every hero needs a threat, a foe, a challenge to overcome. Whether that threat takes the form of a crime boss, an alien with a ray gun, an evil scientist, or something supernatural, is down to the writer and the genre it might fit in.
If I were to point out Johah Hex for an example - a western bounty hunter who's original premise and environment was the Wild West and how he made his living in it from day to say. Anyone with an interest in the Western genre would recognise Hex's world, it is familiar and knowable.
Does this character belong in a dystopian science fiction future? Would his being recast as a 'Mad Max' pastiche be true to his character, his origins...? No. Not to my mind.
Does Hex, a Cowboy made in the Clint Eastwood mold, belong in the 20/21st century meeting modernday figures and meeting Superman etc? No.
But they do it anyway. It can occasionally be interesting perhaps, but it really is not what Jonah Hex is about, it isn't who he is or what he was created for.
The Dr though is used to having to deal with major league threats, so wouldn't bit those type of villains be right into his comfort zone?