I think that’s a question of formality. It’s of course obvious that if all points after each chunk lie above the old diagram, then the line from the origin to the first point does too. Yet, we actually do require the property that that line in its entirety lies above the old diagram too. Depending on how “obvious” something needs to be before you choose not to mention it, it could be considered necessary or not.
I don’t think this works. It is very much possible to construct a (fee) graph N that lies above graph D everywhere, but whose derivatives (feerates) aren’t.
EDIT: I see, you’re talking about average feerate for the entire set up to that point, not the feerate of the chunk/section itself. Hmm. Isn’t that just another way of saying the fee diagram is higher?