How a cashier picks it up out of the drawer doesn't have a whole lot to do with how the cashier hands it over to the customer, though. Taking the bills out of the drawer first never prevented me from giving the customer the coins first.
It's just the way most people are used to doing it then I suppose. For me personally, since I always pick up the bills first I just naturally put the change on top. Seems like one step too many to make the bills be the ones on top.
I usually pick up the bills and then hold them in my left hand. Then I pick up the coins with my right hand. I hand over the coins, and then I hand over the bills.