I would say "don't cry because it's over, smile because it happened", but I'm pretty sure that couldn't apply less to this situation. The quick one month fling with a first ballot, future HOFer has come to an underwhelming and unfulfilling end for both parties. All it took was 81 yards on 27 carries over 4 games for the New Orleans Saints and Adrian Peterson to realize that their relationship was much better in theory than in practice. But hey - at least they avoided the exasperating stretch of stubbornness that generally precedes most breakups and ultimately ends in a resentment-fueled, public scene!
Their one social media-enabled spat might signify otherwise, but this is surely a mutual, amicable split that leaves both everyone involved feeling better about their future prospects. Sean Payton can now give more attention to his younger, more intriguing love interest in Alvin Kamara, and Adrian Peterson can get to playing the (back) field that was left unattended by David Johnson's injury. Oh, what could have been. Oh well, they'll always have...uhhhh...an iota of pre-preseason hype..I guess?
Now, I'm not sure of the salary cap ramifications of this move, but hopefully whatever they pissed away in available money they made up for with the addition of a mid-round draft pick.
Speaking strictly from a football perspective, however, I see very little downside. The presence of a proud player who was desperate to re-prove himself served as nothing more than a ticking time bomb in a locker room that certainly didn't need distractions from the person filling a relatively negligible role on the roster. With Mark Ingram's versatility demanding snaps and Alvin Kamara's play demanding touches, Adrian Peterson wasn't soon to see the field in any significant capacity barring injury.
I do think it's possible he still has something left in the tank, but he certainly wasn't going to be able to do anything more than sit in the show room and rev the engine a couple times per game in New Orleans. Might as well give him the opportunity to run until he's on 'E', and - more importantly - get something for him while it was widely presumed that his value was next to nothing.