That is literally the exact point of reusable bags. The hint is in the name.
And of course the larger issue is the totalitarian nature of this. Who needs two cups of coffee? Ban the second cup! This idea that we should start using the government's monopoly on violence to ban what are symbolic and irrelevant things -- even without thinking through the repercussions for sanitation and energy -- is a very dangerous one.
But you are not making the world better, you are forcing random laws on people as part of an empty performative ritual.
If you wanted to live in a cleaner world, you would focus on improving systems of sanitation rather than trying to force a very marginal reduction in waste going into these systems.
90% of the plastic in the ocean comes from 10 rivers in India and Asia. The plastic is in the ocean because of poor garbage pickup and disposal infrastructure, it's not there because some guy in San Francisco is using a single use plastic bag when he goes shopping. If you want to make the "world" cleaner, then improve the waste management infrastructure rather than trying to reduce plastic waste by 0.000000001%. The thin disposable bags are not gonna put you over the top.
These are all symbolic acts that have real world deleterious consequences in terms of personal liberty as well as increasing the number of food poisoning cases, emergency room visits, etc, due to people re-using bags without properly sterilizing them between each use.
They are due to plastic being a pollutant.