Marrying Sansa off to Robin would be Littlefinger dealing himself out of the game. He's only lord of the Vale until Robin comes of age, at which the title is Robin's. Not that that matters, because Robin's clearly a dead kid walking, but marrying Sansa to Robin would be a waste of time and marrying her to anyone else in the Vale means putting her a step further beyond the child of his (short-lived) wife. Sansa only helps him move beyond the Vale if she marries him.
He could sit behind the walls of his castle, but then instead of manufacturing a reason for all sides to favor him, he'd be giving all sides a reason to resent him. So instead of holing up in his castle, he's turning everyone against each other and putting himself in the perfect position to demonstrate his ability, loyalty, and worthiness to rule the North regardless of who comes out on top, as long as he's there right at the end to help with the final push that shoves whoever's weaker off the edge. You're talking about him making claims after the fact, when what he's working towards is his right being undisputed, self-evident, and singular.
He's not going to sit in his castle and wait for things to play out so he can say, "But look at meeeee!" Chaos is a ladder, bro. Gotta climb it.
