There really is no place for Stormwatch / The Authority in a universe that already has Superman/Batman/the Justice League. Nu52 tried to set up a status quo where Stormwatch took care of the really serious planetary threats while the Justice League were the posers with pretty faces for public consumption...but that just didnt work.
Bad writing is the sole problem.
If Planetary, the Authority, the WildCats can all be in the same place with no problem, then so could have they made it into Earth 1 or 2.
Which leads to the next issue... could have easily just been on Earth 2. it writes itself. Apocalypse invades Earth 2. kills batman, superman and wonderwoman, 80% of the worlds superheroes. Powergirl, and Huntress/Robin accidentally get sent to Earth 1.
There was a running joke for nu52. Seemed every single comic had its own super secret clandestine government organization. I can't even name them all. Checkmate, argus, Stormwatch, suicide squad's organization, Metal men's organization, the one in Firestorm, pretty sure Aquaman had one too, Justice league dark, etc it went on and on.
Earth 2 could have EASILY been home to the Authority. Not just easily. it would have been a perfect fit. In the same way The Authority formed when Stormwatch was murdered by Aliens. (ps, I shit you not, actual Aliens TM vs Stormwatch crossover event comic.)
Earth 2 stuff is a good read though still.
WW's solo comic is miles from Justice League. Batman in Gotham basically can't work within the Justice League dynamic either. one minute Batman is fighting crime and the Court of Owls with his bare hands, the next minute hes building OMAC, Brother Eye and Teleporters... right...