I think they just saw the possibility of having to deal with Shawn Spears in a faction and said "Nah we're good"
From my vantage point, if AEW is doing the Four Horsemen, Spears is a red herring.
He's teamed up with Tully, so why wouldn't he be included?
Well, if I'm reading my AEW tea leafs right, his spot will go to...MJF.
I know, you're saying "Wait MJF just joined the Inner Circle", which is another red herring.
Cody, and FTR, will start reforming the Four Horsemen in AEW.
When they do, Shawn Spears will ASSUME that he's in, via his relationship with Tully.
Not so.
Cody, and FTR with Tully, will turn Spears down for as the fourth member of the Horsemen.
Right around the same time that all this is all going on, MJF, will have secured himself as the new leader of the Inner Circle.
Just like any spoiled brat, he'll already be bored with the Inner Circle when he takes it over, so he leaves them high and dry for the Horsemen after ousting Jericho from the group.
MJF will oust Jericho from the Inner Circle, take the group over, and then say he got a better offer from the Four Horsemen, in short secession.
This will lead to MJF having super atomic nuclear heat with the crowd for him ruining the Inner Circle just for the hell of it.