I don't know if there's ever been a case where a movie or streaming, etc ever had a situation where they decided they can't use X character or X story because the CW is already using them. Usually the other way around. Hell the initial successes of Arrow and Flash are a big reason why superhero tv blew up the way they did, those big streaming shows like Daredevil and Doom Patrol didn't happen until after, I remember when Arrow, Flash and AOS were the only marvel/dc shows. Now the genre ie like cop shows, theres so many you can't keep track. Maybe it would have happened sooner or later with or without the Arrowverse but if those shows fell on their faces it probably would have set the genre back years and years instead of jumpstart it into what it is now. I mean don't get me wrong these shows are inconstistant quality wise at best but clearly a definite and big net win for the genre and dc. Plus they built the closest thing to a functional shared universe in live action that we've gotten so far. I don't know if we'll ever get that in a satisfying way on the big screen.