I think it's worth a week of potential inconvenience to find out.
I don't have strong feelings one way or the other though, people in groups rarely act as you'd expect them to unless you've got a valid sample to generalise from. I'm unaware of any valid sample for what happens when clusterfuck is removed in ZK.
I do think weekly variance could be good. Changing the availability of supported gametypes based on what day of the week it is. Then everyone would know to turn up at particular times if they have a strong preference, which makes these games more likely to happen anyway. For example, I believe more FFA would happen if you could only play FFAs one day a week, even though that doesn't make intuitive sense.
I think we should test it.