No, actually you do it the other way around. Sting returned to put the Authority out of business, failed due to the stupid Cena stipulation and now he returns to finish the job permanently, match stip is if Sting wins, The Authority is gone for good this time.
Too bad The Authority would just be replaced by a different heel power character within a month or two.
If we want to stick to the storyline, shouldn't Bryan be in that spot? Everyone else seems shoehorned in. He should have a handicap match against HHH, Brock, Rollins, Undertaker, Wyatt, and Kane.
If we're going to go down that rabbit hole, have Cena win the belt at Royal Rumble. Have Bryan win the Royal Rumble. Have HHH steal the MITB briefcase from Rollins because Rollins couldn't get the job done at Royal Rumble. Have HHH get the belt from Cena. Have Bryan vs HHH 2 for the title at Mania. If Bryan wins he's champ and The Authority dies.