In general, death penalty in the US, while it gets a lot of attention, is very rarely used. Most people on death row are effectively serving life sentences with extra appeals. Because of the rather permanent nature of the death penalty, the system makes you go through a number of appeals automatically, above and beyond the normal number granted to a person serving a life sentence, and they are pushed through at a higher speed. This means that, because of the cost of a trial vs the cost of holding someone in jail indefinitely, a life sentence without parole is actually cheaper for the state than the death penalty.
Most states also have pretty strict limitations on how the death penalty can be applied, most of the time requiring Murder 1 and extenuating circumstances. (Ex, torture, rape, murder, all premeditated, would justify DP in most states that have it) It's something that varies a little bit state by state, and I'm not certain on California's rules regarding it, but he may not have even been eligible for it.
Oh, and as for giving up his right to appeal, in certain circumstances, such as leading them to her body as part of the plea, then yes, that is something that should be built into the plea bargain. If they were simply going for a bargain for a shorter sentence, and not really doing much more, then it turns into a gray zone. Plea bargains are often negotiation based, so you can go back and forth on some things- in a case where he's already been judged guilty, he needs to have something to offer them.