IMHO, an outright ban is exactly the right thing. The typical person will not turn down a bag given for free every time they visit the store. They get home, unpack and dump the plastic bag. Having people purchase reusable bags makes folks think and actually plan their supermarket visits (how am I going to carry my purchases). In Kenya, single use bags are completely banned, in less than 5 years, plastic bags on trees [1] became a thing of the past.
On the other hand since we don't get the plastic bags for free anymore I'm usually struggling to find a sturdy plastic bag at home when I need one, e.g. to wrap shoes in a travel bag.
No, that's not an argument about not banning them, just a funny observation how these things change. I also used to often not buy any trash bags and just use the decently sized grocery store ones, but maybe in never tossing but reusing them I was already an outlier.
1. https://i.pinimg.com/originals/df/8f/52/df8f52035377cf815650...