TDK is about Batman and Joker's war over Gotham, with Dent representing Gotham. You lose Dent's arc, you lose what the conflict is about; it becomes too abstract and you don't see any direct consequences of Batman and Joker's actions.
I don't know what you mean by "Batman having to choose" is the core of the film. Choose what?
Two-Face alone is not a good enough character to justify his own movie. The idea of Two-Face works best as the third act of a character arc, rather than a completely separate villain in a separate movie.
Ending the movie with Dent just turning into Two-Face, and not actually dealing with the ramifications of that right then and there, also just completely leaves TDK both narratively and thematically unresolved.