During chilling is when I rack the prior fermented beer to keg and harvest the yeast, if applicable, for pitching into the just brewed batch. Then I clean and sanitize the prior fermenter and by then it is usually ready for accepting the chilled wort transfer. I brew very frequently, so making brews back to back is convenient for me.
Occasionally I don't have a beer to rack, in which case, I sanitize the waiting fermenter and wait on the immersion chiller to reach pitching temperature...and, yeah, that is boring.