You make Littlefinger sound like the Joker. He's not. Littlefinger doesn't tear shit down for fun. Rather, he tears shit down because a state of chaos allows people like him to ascend (hence "Chaos is a ladder"). Littlefinger has tangible goals. As for what those goals are, who can say? Lands? Titles? A red headed girl on his cock? Creating the most powerful telepath to have ever lived by mating Sansa and Sweetrobin? Its a mystery.
That said, the books end with Littlefinger in charge of one of the two remaining intact armies in Westeros, the (known) heirs to Winterfell and the Eyrie, claim to the Fingers and Harrenhal, plus a significant warchest. When the show picks up the story, he hands the heir to Winterfell to a psycho, spends his army retaking Winterfell in defiance of the Queen, and then leaves the heir to the Eyrie with his enemies while he dicks with two teenage girls for a few months. Oh, and he dies because his plan rested on the hope that two sisters living in the same castle wouldn't spend five minutes together comparing notes.
I don't mind Littlefinger dying because the house of cards he built inevitably collapses on his head, but holy hell, at least write it so it works without Littlefinger being forced to act like a complete fucking exceptional individual.