Good food for thought. I buy most of my produce at the farmers market. They aren’t affected by the grocery store regulations and still offer plastic bags. I limit my use of them but still use some occasionally. In particular for collecting food scraps and waste that must be segregated from the regular trash but oddly, in my area, can’t go in a compostable bag.
The Wirecutter found the reusable bag best at keeping veg fresh were the towel-like Vejibag that you dampen and re-spritz when they dry out. Just the ticket if you want your veg to have a spa experience. They’re also expensive and bulky but some less expensive draw-string top cotton bags also performed well.
Edited to add that a nice feature of those bags for use at a grocery store is that each has a little tag with the tare weight stamped on it.
I might rifle through my stash of kitchen towels (or pick up some new ones from TJs) and try stitching up some drawstring bags of appropriate sizes. I know the towels tolerate washing in hot water and bleach as I’d want for something like this.
And as others have said, I routinely wash greens and store them wrapped in damp towels.
I’ll report back on how this works.