Have they not already laid the groundwork for warming those seats with non-anointed company men?
Helpers?
I think they have their 'continuation of religious government' plan already worked out.
Anyways, if these guys are not really calling the shots and are just figureheads (as has been asserted), then I don't know anything would change upon their demise. The same sinister forces would likely be in play behind scenes.
Best we can hope for is a strong personality to rise up and try to take control. I think we are due for a schism.