honestly, I think it is still much better. Ask the person if they already have a reusable bag they'd like to use, etc. and if not ask if they'd like to buy one or that they do have plastic avaible
I bet that would cut down a lot as people would now have to consciously think "yes, I will not use a reusable bag I will take a plastic bag I know is not the best for the environment" vs "you know what, I have room in my backpack and don't really need a bat or I could just carry it"
Will it reduce bags as much as if they totally got rid of them? No, but I bet it reduces them a lot without the angst of taking it away/forcing people to pay for a reusable one