I feel for ya. Perhaps the answer is getting lost in translation.
Do they realize that a "Pool" of servers is 1,2,3,4,5 + Servers and that if one of them is down, that you don't need to kill the rest?
Most people just want to view the F5 as a "Black Box" and only know what they want, but have no clue how to get it.
I would ask them that if you want to take down all of my servers that are hosting the website, what do you want to show the users instead? Then implement the iRule above and tell them to test it for functionality.
Hope they figure it out....