Firstly I now have to buy garbage bags, where I previously reused shopping bags. That completely negates the benefit. But let’s ignore that and say most people just trash them.
Even in that case you’d have to reuse a reusable bag 20 times to break even. I don’t know about you, but on average maybe I get 0-5 reuses out of these bags. That’s just squarely worse off than we were before.