Not cotton, but here is a linen and wool comforter

Tbh yeah you’re going to have most luck with a duvet. Vast majority of comforters on the market are a down alternative fill, wool is considered more of a niche material. Wool is often not machine washable anyway so you really should have a cover on it anyway so it doesn’t get dirty. If you don’t want to deal with taking the cover on and off that often just use a top sheet.