I think it works because while Perez's Minerva was cool and creepy, an easily grasped motivation and connection to Diana never materialized. You always knew what Priscilla's deal was. Rebirth took the best elements of both and combined them into one much better character (though I think the Alex Ross update for Priscilla could work on its own as well). It's a cliche, but most of these characters are the ones who invented the cliches in the genre. Diana did know Priscilla a bit before she turned, so this is really an expansion on an older concept being re-worked into a modern version.
There is that problem with Etta and while I'm not wild about Rebirth Etta in general (a lot of her scenes could be swapped out with Michaelis and Darnell and you'd not notice the difference), the focus on Julia in the Perez run created the exact same issue. Diana and Etta were never as close as they should have been in the post-Crisis era. The main thing I'd change in post-Crisis and Rebirth is swapping out Etta with her Holliday Girl incarnation, who actually is distinct.
Julia wouldn't have to be superfluous at all though. Barbara was only with Diana for a little more than a year before she was cursed. No reason at all that Julia can't be brought in as her replacement and they could form their own unique bond. It was on Robinson that we got what we got.
I wouldn't say Barbara was completely manipulated. She had choices along the way she could have made that she didn't. Diana warned her and she didn't listen. Cale and Godwatch gave her the funds and kept Diana out of the way, but they may have just sped up the inevitable. Comments from Urzkartaga indicate that he and Barbara made a bargain and it only went south when he discovered she wasn't a virgin and so cursed her, but before that she was on board. Later she "surrenders" herself to Cale when there is no immediate need to do so because she wants the Cheetah power back without the drawbacks and is willing to believe Veronica's lie, and then puts all the blame on her and denies her own actions. She's not a reliable narrator and deflects blame onto others for some stuff that is her own fault.