An ending in which Bruce died would go against many of the points and developments in the film.
The film was a journey for Bruce/Batman, with him getting an epiphany in the prison scenes that death was something Batman almost embraced since he had no fear of it and that death should not be the end result, it did not make him stronger than having no fear of death. This was emphasised by Alfred earlier on in the film too. It was a stronger ending with having him accept that he could let go of Batman (kill Batman in a sense), pass on the symbol and cowl to another and live his life (whatever was left of it). That was a much more powerful ending than simply dying in the expected self-sacrificing, brooding and dark manner the entire trilogy has pedalled his character as. I think it would have been too grim as well to the point of desensitisation: he lost his parents, he failed Harvey, he lost Rachel, he took the blame for Harvey's crimes, spent 8 years as a broken recluse, got his back damaged by Bane and finally emerged from that pit after that personal development in believing that he wanted to live - if you take all that and then kill him off in some sacrifice, it doesn't payoff very well.