I am guessing Dean, Robert, and Eric have some stuff to deal with before they ever think of what is to happen with STP. The scenario that I can foresee, if they do go on, is in a year or two getting back together with Chester. In a weird way, Scott's death legitimizes an incarnation of the band with Chester that goes beyond an EP. I know that sounds like blaspheme, but what I mean by that is Alice in Chains fans are more likely to accept William since Layne is, sadly, gone.
In a year or two, we might be anxious for some new music by Dean and Robert and Eric, and maybe everyone would be ready to celebrate the legacy but also make some new music. I'm an AIC fan, yet some of my favorite songs are with William. To me, the hardest part of accepting songs like Black Heart and Tomorrow was that I always thought Scott would sound better. But to be perfectly honest, those are songs that stand up to the STP legacy.
I will no longer be thinking, 'What if?' when listening to the Chester version of STP. I realize more time passed with AIC and Layne, but no situation is perfectly analagous. Chester is such a fan and such a good performer, and you could tell he was making strides singing not screaming. To me, the only way it goes forward is with him.
Anyway, it has to be hard for Robert, Dean and Eric to have shunned Scott and 'turned the page' and then have him end up dead at 48. I am guessing there is some grieving that must go on. I am sure they will second guess their actions. Second guess things they said. This will haunt them forever. We think Tommy will be haunted, think about the guys who knew him for 30 years and turned their back on him 2 years before he died!
Let some healing happen and we all might be open to a new era with Chester.