The standard nitrox mixes reduces nitrogen loading in your tissues by containing less nitrogen than air. Therefore, the advantage is either (1) that it lets you have longer NDLs for a given depth, or if you dive air tables while breathing Nitrox (2) theoretically reduces the risk of decompression illness for a given profile.
The latter approach is a bit controversial, given the fact that "undeserved" DCI hits are rare, and it's hard to get enough profiles together to prove this in research - you would need to have two large groups of matched profiles with one group on air and one group on nitrox to see a significant difference if one did in fact exist.
The third reason why people dive Nitrox is that some people feel that they feel less tired as compared to air. I'm certainly not a qualified hyperbaric doc, but from what I can tell there isn't much science behind this, and a potentially large placebo effect. That has been thrashed out here in the forums as much as split fins or Spare Air, and I don't have much more to add.
The benefit that you mention - accumulating nitrogen over a long week of diving with big surface intervals between the dives - is also not something that I have seen literature support for. Nitrogen does not seem to have the sort of cumulative effect over longer periods of time that oxygen does (as in the oxygen clock). Nitrox as you know is limited by operating depth, so you would need to study people who are doing many many relatively shallow dives over a long period (maybe dive resort DMs or something?).
Bottom line, if you are limited by gas and not by NDL, I'm not sure why you would dive Nitrox (leaving aside the third reason above). On the other hand, as you improve your air consumption, you may be hitting your NDL soon! Keep at it...
Mike