If Ned sat on the throne, Viserys Targaryen could have taken the kingdom back easily by talking Ned into betting it on the three cups and a ball game.
I don't think Ned Stark would even play a game in the first place.
I think it's more that the others are grandmasters of politics and backstabbing while Ned wasn't trained for that arena and through the normal course of events should have been nowhere near Kings Landing and not even Lord of Winterfell.
You're right; you could take the kingdom from him with "guess how many fingers I'm holding behind my back."
Now four seasons into it, I understand why Ned Stark had to die. I don't quite take the cynical viewpoint that the setting was just too evil for a truly good man. I think it's more about what happens to the characters surrounding him when you kick away the moral compass. Not just his children, but also Littlefinger and Varys and others who were indirectly guided or held back by his influence.
If anything, I think A Dance With Dragons showed why Ned's qualities are very worthwhile in that world.
Are you thinking about the rampant cannibalism, or how most of the Northern lords went along with the Boltons?
I suppose that depends on if whether or not Renly still wanted a crown for himself, and acquired the backing of Highgarden. Stannis' forces are paltry, and the true strength of the StanNed Coalition would be the North. But Highgarden combined with Storm's End was 100,000+ troops, so they're still a huge obstacle. Plus, Renly is always being such a little **** to Stannis.