(Spoilers Extended) Plot hole with the Warden of the North

What was the point of Littlefinger brokering a deal with Cersei to be named Warden of the North if he was going to turn on her anyway and declare for the King in the North? I mean, the show hasn't explicitly stated that Cersei knows he's hanging around Winterfell, but Cersei commanded the Vale Army to attack the Boltons, and after they succeeded, they stuck around and declared for Jon. Obviously, whatever deal Littlefinger had has been rendered moot.

So what was the point of it all? He easily could've brought the Vale Army without Cersei's order. In fact, it doesn't look like he told anyone that she gave the command. As far as the army is concerned, they showed up to save Sansa, not to follow Cersei's orders.

I think this is a certified plot hole. Littlefinger's Warden of the North scheme had absolutely no aim or purpose. It seems like D&D just want us to forget about it.