Brandon Stark kills Petyr Baelish in their duel over Catelyn. Westeros rejoices?

Pretty much – depending on who you are.

Jon Arryn lives, Eddard isn’t made Hand, Bran isn’t crippled, Sansa stays the hell away from Joffrey, Cersei is exposed by Jon Arryn and Stannis, there might be a brief war against the Lannisters, Robert marries Margaery (who’ll have her work cut out for her), etc. 

In more structural matters, I’m of the opinion that the royal bankruptcy doesn’t happen because it wasn’t real to begin with. Sure, Robert will run up some debts, but without Littlefinger embezzling state funds (including, I believe, most of the money loaned to the Iron Throne) and committing massive accounting fraud, those debts should remain manageable, especially with the deep pockets of the Tyrells to finance them.