That's reason 1A I've dropped out - the timeframe is too short.
That would spell disaster from where I'm sitting, trying to plan for one period while still cooking for another...that's a game-killer, which brings up reason 1B why I dropped out...the aggressiveness of the game. The short time I did play, I didn't feel like I was in a fun game, I felt like I was on the factory floor, trying to rush to an impossible deadline.
1A + 1B = 1C, the third part of why I dropped out - with the short timelines and constant pushing to get the next game started, it took me, what, just the second or third game to throw up my hands and quit, because I couldn't keep straight what recipe from which cookbook was for what week.
Personally, what makes sense (with any game, really) is to do it monthly. It's a natural break, it's easy to remember, it's plenty of time to get things sorted.
That's just me, though it might explain the lower-than-expected participation. I do think the concept of the game is a good one, I just don't understand the push for such a relentless pace.