The issue I have is when people mistakenly assume that something can't be, to use your examples, High Fantasy and Gothic Horror.
But those distinctions are given shape by their boundaries. For those two, High Fantasy is all about uncovering legendary artifacts and Horror is notorious for leaving you desperate and under-equipped to face the coming threats. A small choice - the number and types of treasure handed out - but it makes a big difference to the feel of the game.
For many years I was primarily a Hero System player. There, the same mechanics are used for all genres. Limits are then placed (or recommendations given) to achieve the flavor that you want for the story you want to tell. A Fantasy Hero game would be set up a little different than a Star Hero game, and both would be different from Champions. Even Champions with characters like Superman or Green Lantern would be a little different than Dark Champions, a street-level game featuring "normal" characters like Daredevil or Punisher.
Same goes for D&D. There's nothing wrong with certain characters, or certain types of characters, but including them would change the theme of the game. When I pick Dungeons & Dragons, it's because I want dungeons. And dragons. If I wanted to play with guns, I'd play d20 Modern. If I wanted aliens, I'd have picked Star Wars.
If you want to play an alien in a D&D world, you'd have to be really careful with the "coat of paint" such that it doesn't clash with everything around it. If you wanted to play a scientist, some care would have to be taken to make it compatible with the tech level of the rest of the world.
For flavor that's not traditionally medieval fantasy, it should be best left to the individual character when modeling a fantasy game. If you want to play a being from the Xandar system, accidentally stranded on Faerun after a freak portal accident, you add that detail and have the GM/group approve it. Or if you want ties with the Far Realm, add those yourself for your character without forcing it on the rest. The base class designed for everybody should be something a little more harmonious with the world it's being placed in.