According to the IMDB Trivia, Linden Ashby (Who plays Johnny Cage) no longer wanted to be involved with the franchise after reading the script... which.. makes a lot of sense.
Apparently production of the first movie was gruelling, with a lot of reshooting and recasting; Cameron Diaz was the original Sonya Blade, but broke her wrist whilst training for the part. Brandon Lee was the original Johnny Cage, but when he died they simply recast, despite the writers wanting to remove the part 'in honor' of him. It seems they didn't really want Johnny cage after that.
Ashby was also apparently heavily involved in rewriting parts of the script to make the film 'edgier' and 'cooler', and built up a lot of resentment from the production team in the process. In his words:
There was just a lot to improve. And we sat down and we reworked the script to the point that I think the writer was not really thrilled with us. I remember seeing [screenwriter] Kevin Droney at a Christmas party after the movie had come out. And he introduced me to his date and goes, "This is the guy I told you about. This is the asshole that ruined my script." (Laughs.) I was like, "Oh, hi." It wasn't a script to write home about, and we worked hard on it. We didn't write Hamlet or anything, but we had a lot of fun with it.
Why he wasn't recast as per Raiden is another question, but it seems production didn't see the need for the character to continue...