From a workflow standpoint, the head coach not being an offensive or defensive play caller gives the head coach the advantage of not having to build stay focused on play calling and adjustments to play calling during the game. They can be more emotionally reactive to plays and players, because they don't have to move on to calling the next play.
There was a time when the best NFL head coaches didn't call offensive or defensive plays. They were true team and game managers who could focus on the big picture without getting bogged down in the weeds of the offense or defense.
I hope this situation works out with Rizzi, because when teams are successful, their coordinators get hired as head coaches. If Rizzi works out, then he will have an advantage in attracting new coordinators, because his offensive and defensive coordinators will both be calling their own plays.