1) My bin liners do come with handles. Really convenient for tying them off. If I was stuck and for some reason I needed a plastic bag for groceries I would certainly take one. (I use them for carrying the occasional inconveniently-shaped object anyway.)
2) You don't have to use "large trash cans holding large amounts of trash", I have bins of sizes from about 1 metre tall (kitchen nonrecyclables) to about 30cm (bathroom trash) and I can buy bin liners that neatly fit all of them.
3) Why on Earth do you have to leave your cloth bags at the front desk? We're just allowed to carry us around with us as we shop.
4) If you're coating your bags with things that cause disease you are doing something horribly wrong with your shopping. I have to machine wash a bag now and then if an item breaks but that's a quarterly chore at most, and just involves throwing it in when I wash my kitchen towels and cloths.