That these cases are time-consuming is no reason to alter the law. It is debatable whether the death penalty deters crime. It is difficult, if not impossible, to know whether the threat of execution causes someone to stop before committing murder. Moreover, it doesn't matter. Deterrence is by no means the only reason to impose any criminal penalty.
Justice is more than a Pavlovian system of punishments and rewards set up to mold behavior.
It also is the means society uses to make wrongdoers pay for their crimes. And there are some crimes for which life in prison is simply inadequate. It would not have been justice to sentence serial killer Ted Bundy to life in prison. Danny Rolling deserved more than a life sentence for the Gainesville murders. Finally, there is the argument that the state can make mistakes and that it has executed innocent people.