Being as Rush knew his time was coming, he probably made arrangements on how the show should carry on after his death.
Everyone knows who the fill-in hosts were. None of them measure up for the long term. I don’t think the successor is anyone who is known by anybody. Any audition will only take a week or 2 to see if the he/she has the staying power. The late Lee Rogers would have been my choice.
That’s another thing I was thinking. I wouldn’t be a bit surprised if Rush had specific directions for continuing the show over his preferences for his own funeral.