That's not true. Each show has its own separate writing staff, all working under Berlanti and Schechter as the heads of the production company. Supergirl is run by Ali Adler & Andrew Kreisberg, The Flash by Aaron & Todd Helbing, Legends by Phil Klemmer, and Arrow by Wendy Mericle & Marc Guggenheim, and each set of showrunners has a different slate of staff writer-producers that they coordinate. Essentially the writing staffs are the "editorial teams" and Berlanti and Schechter are like the "executive editors" they all report to. They try to coordinate the best they can, and they actually do a surprisingly good job of it given how complicated the task is, but it's unfair and dismissive of their hard work to assume they're all a single staff and that coordinating the shows is easy. They just make it look easy, because they've spent years learning how to produce television and because they're really dedicated to tackling what's really a monumental challenge. But that doesn't mean it's a good idea to make that challenge even harder with unnecessary complications.
Any idea when/why Berlanti stepped away from showrunning Supergirl (because he was doing so with Ali during Season 1)?