I don't think the timing of the plea deal and acceptance is accidental. The judge said no more delays, no more spaghetti-on-the-wall SODDI fantasies. Just the evidence we know is enough to convict him, let alone all the other evidence that would have come out at trial.
It's understandable that some or all of the parents want the death penalty. But that would mean appeal after appeal and some might not live long enough, since the average time from sentencing to execution is around 20 years. And every hearing would argue his innocence, over and over. People recover from the murder of a loved one; it's a trauma that doesn't heal. My psychologist friend says it's like a wound in a tree that doesn't kill it. The tree continues to live and grow but the wound is still there. My argument would be that every time BK filed an appeal on the death penalty, it would trigger every other wound made by these murders. Over and over. And of course, there had to be concern for the surviving housemates and the other young people who would be called to testify and relive the killings.
And finally, there is never a guarantee of a conviction or that a verdict isn't overturned on appeal. And even some plea deals can be mickey-moused by a bad judge, as the Rhoden killings in Ohio have shown us. The plea deal puts this monster in prison, 4 consecutive life sentences plus the burglary. He can't appeal. He'll never get out of prison.