I've been through a lot of different loot systems over the years of managing guilds.
One of the biggest problems I always found with predetermined, transparent council systems is that they only work if you have a whole guild dedicated to raiding and progress for the fun of raiding/winning. It's great for competitive guilds full of competitive people... but as soon as you try to implement such a system in a less competitive environment, you start to run into people a lot more motivated by loot and rewards.
The system starts to have problems at this point. For example, you get people simply not turning up for raids ("My sister's dog's uncle needs me to babysit his guinea pigs and I have an exam tomorrow so I need to also study all night") or being "late" when they know they won't be getting anything that week.
For such guilds, having some element of randomness (via rolling/bidding) or attendance reward (via DKP/EP/other points) to encourage joining each raid helps a lot.