As great of a movie as Seven was, the title alone alludes to its biggest monetary pitfall: there was never any room for a sequel. Seven follows two detectives hunting down a psychopath, one whose heinous crimes are themed around the seven deadly sins. By the end of the movie, the criminal is dead and one of the detectives is mentally broken due to the grisly murder of his wife. How might a studio expand on that to justify a sequel? Should they simply call it Eight, inventing a new sin and a forced plot to go with it? Or have it revolve around a different set of seven items? Either way, it's already sounding a bit hokey, if not blatantly lazy.
Of course, there's always the alternative path of continuing the dreary stories of detectives David Mills and William Somerset. However, that's a sequel route posing so many of its own challenges that we'll analyze this option individually further down. In short, it would've been an uphill battle.
The only way to do a satisfying follow-up to a movie like Seven would be to make it as unrelated to the original as possible, which would paradoxically defeat the whole point of it being a sequel. This no-win scenario starts to paint a picture that explains why the seven deadly sins never fostered anything beyond one great standalone David Fincher thriller.