It depends a lot on the state that one resides (or incorporates) in. With LLCs they mostly all follow the same pattern and if you're the sole owner they can be done without charter, initial incorporation docs, etc. With coops, some states follow uniform common law LCA (limited cooperative association) laws and allow worker-owned coops pretty easily (although lawyers are generally less familiar as they're rarer). Other states only allow certain kinds of coops and require charters and organizational documents. Basically, any time you involve more than one person, there is some paperwork (LLC or otherwise). Coops have this, plus the added difficulty of not being uniform around the US.

Last I looked, Colorado and IL had a lot of coop options to choose from, but nothing was as straight forward as an LLC where you just file 1 notice with the state and pay 100 bucks. LCA states are close, but you still have the "many people" issue.