I'd rather not see Punk lead another faction but he is literally the only connection to The Shield that has ever been teased
You know, I'm partly concerned that it won't even matter to WWE if an actual connection has already been established or not, or even what that connection was in the first place.
Remember half the clues they would tease people with each week with the Anonymous GM (e.g. him "not liking Bret Hart" amongst other "clues") only to completely ignore that and make it Hornswoggle? Or I vaguely recall there being some kind of huge plot-hole regarding the whole C.O.O. storyline involving Vince (perhaps someone remembers that part more than I? I recall there being a strong contradiction that annoyed a lot of people).
Whatever the case, my point with it is, the creative team or perhaps the higher ups in WWE aren't always committed to or concerned with whatever details have been established when deciding what they want - there's a chance they could come up with some mediocre last minute excuse just for the sake of adding someone to the group, or even just go the simple route of simply adding someone without a real reason or
proper motive.
Honestly with that in mind, I hope they just leave it as is for now. They kind of work better as that outside faction and there'd really be no need to change things at this point in time. There's a lot more they can stand to do as is.