Rayon is the best fabric. It's softer and often more durable than cotton, more biodegradable, and these days can be made without using or resulting in toxic pollutants like the original process needed.
I can barely find any 100% rayon clothing and it frustrates me greatly.
I think the breathability depends on the tightness of the weave, but yes unfortunately one of the main downsides of cellulose fibers is that they don't wet very well and thus don't wick moisture much at all