#1 Sister Abigail is an element of Bray Wyatt's past
I strongly recommend that you check out this podcast with Korey Gunz and Tom Colohue of Sportskeeda who offered their own unique take on why Liv Morgan should not be the new member of Bray Wyatt's Firefly Fun House.
A female WWE star said her life is in danger. Details HERE
One of the major arguments raised was that Sister Abigail is a part of Bray Wyatt's past and not his new and improved persona.
As much as one can call The Fiend an extension of the erstwhile 'classic' character, I think it's safe to say that Wyatt has done much to distance himself from his earlier gimmick. Yes, he's still supernatural but now he's a brand new supernatural being.
It would constantly be looking into the rearview mirror to have Liv Morgan appear as Sister Abigail, I feel. Plus, I do believe it was established that Sister Abigail was Wyatt himself, in a woman's costume.