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.

1. https://i.pinimg.com/originals/df/8f/52/df8f52035377cf815650...