This is something that has crossed my mind.
The ideal thing for a composer is not to be typecasted of course, but I see more and more in Hollywood, that that's the norm!
As a starting film composer, if I ever would be typecasted I'd like to be in the romantic period drama genre.
I feel it's the closest to my general style and character, and it's the music I'd love to compose most and that moves me the most.
What is yours?