Woven, Non-Woven Bags, Polyester, Nylon etc. Bags though they are not compostable Bags they compensate indirectly in helping the ecosystem, because Bags made of these synthetic materials are reusable for a long time, so in the face of single use Plastic bags, which are used one time and thrown away, this proves better. Meantime, these bags are cost effective and commercially viable.
In the case of cotton bags, it is eco-friendly and it originates from nature and returns back to nature after serving the purpose multiple times. Think of this taking into consideration the cost effectiveness of various Carry Bags, of course, there is difference, cotton, Jute and Juco etc., costs much higher than the carry bags made from synthetic material. But, same can be worked out more productively by manufacturing cotton Bags in large scale and thus cost significantly reduces, so these bags can be made available on low cost to people and will serve the very purpose affectively. Thus environmental sustainability attained.