I'm not necessarily opposed to it, but I also don't see a blatant purpose so far besides padding the game (a major complaint in Zelda these days). Awesome as Majora's Mask was, I actually hold the limits of its three-day cycle as a negative point. Want to play at the shooting gallery for kicks? Too bad - third day, it's closed. Gotta go back in time and lose your supplies if you want to go there. This was mildly annoying in a three-day form, so seven would probably be pushing it.
Even if you could quick-travel to the time you wanted, I still don't see how it would aid the game much. Perhaps it could lend a sense of realism when, say, one shop is closed on weekends, forcing you to improvise for the time being. This is mostly reliant on the game mechanics being better-developed themselves, though. Actually, now that the creative juices are flowing, a weekly cycle could offer some benefits. What if an unspeakably powerful and horrific creature wandered the town at night during one day of the week, but you could only complete certain sidequests or gain specific items in that place during that period? Things like this could, in addition to providing realism, promote strategy and risk vs. reward. Do you want to brave the dangers of the mountain on this day, or wait until the danger shifts into something you're more comfortable with? Monday makes you rely on stealth, but Tuesday pushes you to work quickly since an unstoppable monster chases you around that area.
Actually, this is a pretty good idea. We should continue this topic.