Most of the plastic involved in getting food from farm to home isn't the carrier bag or even the food wrappers. It's the massive amount of plastic that pallets of goods are wrapped in for shipping, which happens several times throughout the supply chain.
We should focus on the latter, instead of the former. Pretty much all we're doing is virtue signalling and maybe hoping that it'll make a tiny difference.
Heck, even a marginal improvement in fuel efficiency of trucks delivering to grocery stores would probably do more than these plastic bag shennanigans.