What if Jon Arryn died in 291 AC, right after the Greyjoy Rebellion?

Bran’s just born, no Rickon yet. Robb’s around 8, Sansa 5, Arya 2, Jon 8, and Theon’s still new at Winterfell.

If Robert comes north and asks Ned to be Hand at that point — when the realm isn’t totally falling apart yet and the Lannisters don’t control everything — what do you think changes?

Does Ned even go south? Or if he does, does he actually manage to hold things together? Would the secret about Cersei’s kids come out the same way, or later?

Curious what people think this version of events would look like.