I don't know that "The Crow" is the best parallel. FYI, Lee died before shooting was even finished.(he was killed onset with maybe only a few days left to film) They almost didn't bother to finish it, but ultimately did it to honor Lee's performance, so that people would actually get to see it. (there might have been studio pressure, but I have no info on that) But that's really neither here nor there...
The two biggest differences is:
1) The character's story was done. Of course there could have been a contrived reason to bring him back, but even in the comic, it was a complete story of one man avenging the death of himself and his fiancee. It would've been hard to think of anything else that would have been as personal.
2) The second film had a different director. Alex Proyas is one of those directors with a signature style and vision so any second film with a different person at the helm wouldn't have been the same either way.