Agree that a line diagram would be helpful, but I don't think there will be one forthcoming. Each camera could have a slightly different process and certainly different amounts of noise added at various stages.
And as I understand it, true iso invariance would have no penalty at all. But I suspect that in practice very few cameras are truly iso invariant and that there will always be some difference between noise in an image shot at high iso and an image brought up in post.
As for advantages, one of the primary one's I've heard is regarding insurance against not blowing the highlights. Many people practice ETTR to maximize data gathered, but this risks having something overexposed and clipping the highlights (which can't be recovered). By exposing a bit lower in-camera your much less likely to clip the highlights and if the camera is iso invariant then you're not even paying a penalty to bring up the shadows in post.