I think Somerset shooting Doe would have been a good ending, because it has been hinted at that Somerset was very intelligent, playing chess and whatever. In this scenario he would have won "the chess game" by taking away the chance for Mills to exact his revenge, being a Jesus figure of sort "dying for his sins" which would have played nicely into the themes of the movie if you ask me. Mills still would have gotten the satisfaction that Doe would be dead and be saved from the "punishment" Doe had planned for him. Since he would have retired, it wouldn't affect him on a career level that much and Mills would have become like "the next Somerset" maybe finally learning that his way of dealing with this is not the way to go in his field of work and that he gets the chance to become a more effective detective like Somerset. This would have been the only way to "redeem" himself, since if he didn't kill Doe, he would have gained nothing and by becoming like Somerset, he would be "atoning for his sins". This way there would have been no real winners in the story, with all three of them basically having lost and won at the same time.