I think that is possible. My mother has had the same cotton canvas grocery bags for ~40 years. They are faded from washing, but are still strong, and she still uses them.

The other advantage is that cotton bags do not shed as many microplastics (the thread is almost always synthetic).

Many of the "re-usable" woven plastic bags I've acquired in recent years are of extremely poor quality. I have had to re-stitch many of them, and some had to be discarded after a very short service life.