Our local supermarket has a bin to recycle these bags. Most probably don't use it, but we do! Certainly is better than single-use paper.
Back when we went to the recycling facility in person, we would pre-sort and still use the paper bags.
I suspect, when used this way, paper beats plastic, environment wise (of course, there are better alternatives, like personal canvas bags, but that's another story).
http://www.allaboutbags.ca/papervplastic.html https://science.howstuffworks.com/environmental/green-scienc...