The main reason is that you would want to tribute the thing you're making a fangame of, hence fangame.There's two semi-reasons to make a fangame:
it only took me a little while to figure out that there's no reason to make a fan game when you can make an original game.
- You can get music and graphics already complete from e.g. tSR and get to coding the game at once
- You get bonus attention from people liking the original game
At least those two reasons are what keeps making me embark on new fangame projects every now and a while.
Note; nobody should think that fangames have to be a "clone" as in, trying to remake a game. Tributes to shows, movies, books, games, etc can have many forms. Including this.