In the states, the showrunner is a leadership position. Usually it's given to people with previous showrunner experience or writers who worked their way up the ranks. All 3 showrunners from Modern Who had both criteria. Davies brought back Doctor Who as a passion project. The BBC wanted him for his experience with Queer Eye and Second Coming. Moffat was a sitcom writer famous for Press Gang and Coupling. Chibnall was known for Broadchurch.
Most of the big names or obvious choices are already taken. So we'll probably deal with an unknown/dark horse choice.