The war of kings showed that Tywin is a wiley asshole and could just make a bunch of phonecalls and have a bunch of dudes have his back just off the promise of paper(even though, ironically enough, they were bleeding money).

The North showed they could do that just based off that fact that they WERE one kingdom once, still have some beef with getting herbed out by dragons, and Ned is truly beloved. Notice they lost when they didn't play the politic game right with with their bannermen after having a superb run.

While the sand snakes and fam are having fun looking sexy, being rich, and being some of the best fighters in the realm its not about that.

Plus, ultimately, the Vale getting involved would have shown Littlefinger's hand waaaayyyy too early since he would have eventually had to come out publically with Lysa when she declared war.

Keep in mind the character didn't see the exact end game happening, but him replacing the current Hand with someone who he thought was more mallable and or stupid was a good move, period. WORST case scenario if none of that ned shit happened I would have went to the Lannisters on some, "Yo, Aryn was gonna talk about y'all being an incest family and I handled that, remember me" and just kept that in my pocket until something else popped up. (A natural baratheon heart attack? death from syphillis? lol)