Not saying don't but,
Tried this type of arrangement with a couple friends and relatives many years ago, as I'm always looking for help.
I had the wood delivered to my processing area as I had the connections to get it at a better price. This was mistake one, as only one person reimbursed me for their share of the wood. I found there's no way to deposit promises to pay in the bank. Couple of them would come in the landing and grab a load when no one else was there. You guessed it, same ones that never paid for their share of the treelength. A change of lock on the gate at the entrance fixed that.
Second issue was getting "the co-op" to arrive on time, or show up at all. Those that arrived wanted to play chainsaw, splitting and loading were not on their list of things to help with. Amazing how much work they could watch while talking on the phone. Leaving early another biggie. Once their truck was loaded they suddenly remembered somewhere else they needed to be.
I'm not saying this type of arrangement won't work, more power to you and your group if you can make it a success. In my case it was a one and done learning experience.
Take Care