If California has a problem it isn't because bag bans don't work, it's because they've screwed up their implementation.
And yes, supermarkets do still use a lot of unnecessary plastic in packaging, but that's another issue that can also be tackled, and I haven't seen evidence that it has actually got worse since the plastic bag levy.
Arguing that plastic bags shouldn't be tackled because something else could be done is an argument to do nothing.
Plastic carrier bags were an absolute scourge a decade ago, they were everywhere. Their use has been absolutely decimated.
The arguments that people are secretly using more because they're no longer re-using them as bin bags or because they're buying "bags for life" instead are bad faith arguments that just don't hold up to the statistics or the reality of the situation.
Over 7 billion less plastic bags produced per year in the UK. That's a tremendous achievement.