In the flash-forward Team Arrow, the four members — Mia, Connor, William, and Zoe — are more or less on equal ground, which means that somebody stepping up as leader could result in some friction.
Original Team Arrow had a clear leader, as it was Oliver’s mission to begin with, and the rest joined his cause.
And then, of course, there’s the issue of Connor’s seemingly villainous adoptive brother, John Diggle Jr.
Although Diggle and Felicity never blindly followed him, he was the Green Arrow, and they didn’t even get code names for a few years.