I have spent a lot of time now rerunning all of my D800 tests on a D4 to compare.
All of the lenses except my 85/1.4 are much better behaved -- less correction needed, but more importantly at different distances and focal lengths they are much more similar.
As a couple of examples, my 24-70 averages a -5 on the D4 but had values of (-1, -2, 3, 0, -5, and -15). That -15 (which I did 3 times!) was very different, but the QOF between -15 and -5 was only about 10% - very flat falloff.
Compared to the D800 they were -1-, +7, -8, and -19. IN that case the -19 compared to say zero was down about 35% in QOF, so it's a much steeper difference.
I don't want to clutter the topic with charts, but if you line them up and draw a line down them, the D4 charts are much more nicely centered around that line and much flatter (fall off less sharply) so it is easy to pick a good average value. IN fact on most lenses zero is not a bad choice -- not ideal, but not bad, and I understand why people might say "I never fine tune my lenses".
The D800 not so much, they vary more, and the fall-off is stronger so that any compromise value has (at some distance or focus) a fairly soft value. Will it be better if adjusted? Is the sharper falloff a natural side effect of more pixels? I have no idea.
The D4 also has a much more consistent set of focus points (though hardly perfect, and the worst point is bottom left (.61 on a 24-70, left/center is .76). But MUCH more green on it.
Overall I will say that doing the same calculation on a D4 has left me feeing both that my D800 does need adjustment, but also that Focal is perhaps not accurate enough in some cases, and it may be showing more problems than are real. See my other post on the 85/1.4 and how it seemed to misread heavy CA for better focus, and IMO just gave the wrong answer (on the D4 -- similar if not more erratic results on the D800).