Who are you signaling to? People who care for the environment likely know how stupid it is that they have to spend a few extra bucks when they forget their bags and have to buy thick plastic bags they'll throw away. I've never met anyone in real life that thinks this is a good idea, regardless of their politics.
Hello, it's me, the person you've never met in real life! I'm real, and I live in New Jersey, and I'm super in favor of this law (paper bag warts and all)
You're right, in the short term a law banning plastic single use bags likely results in an increase in the number of multi-use bags people buy because they forgot. How long do you expect this cycle to go on for? I'm going to imagine it's "a few months" for most people, before you start leaving a couple bags in the back seat of your car. People are pretty clever and adaptable. It's akin to saying that we need to ban new calendar years because everyone writes the old calendar year for a few days in January. It seems pretty reasonable that people can and will, broadly speaking, remember their shopping bags.
The bottom line is that the tragedy of the commons is in full effect when it comes to plastic generally, and plastic bags specifically. We got addicted to them, and they're terrible. I'm going to write this one more time: We got addicted to them and they're terrible. Short term financial gains for long term environmental pains. We should have never switched from paper bags, but plastic solved a lot of problems, and nobody seemed to notice or care about the waste issue. This law itself may not be "fixing" the issue entirely, but it's forcing consumer change and that pain alone might helpful in solving the issues long term by forcing people to think about the topic.
The problem is a lack of education more than anything. People simply believe that plastic = bad, despite the fact plastic bags should probably be about the last plastic thing banned. Plastic bags take a miniscule amount of energy to make and can be thrown away and captured in a landfill indefinitely after that. Now we get varying levels of "reusable" bags that cost more economically and environmentally and the break even point is basically non existent. "A few months" of forgetting bags means the average person likely consumed more energy in reusable bags that weren't re-used than years of plastic bags. Plastic bag bans are spending dollars to save pennies, most of these laws really just make people feel better rather than provide actual benefits.
Want to save the environment? lets focus on electrifying power tools and standardizing batteries so there is less gas used and e-waste. Let's encourage insulating old buildings. We should reward reduced packaging, more bulk purchase options. Doors should be required on coolers in grocery stores. Require greywater systems in new or renovated buildings. Mandate usage of native plant species for lawns/green areas. limit dilution of water based products.
People who care for the environment enough to know how this stuff works are a drop in the bucket compared to the number of mostly uninterested people who wanna look like they care or think they care (because it's fashionable to do so) and can be hoodwinked into thinking that banning paper or plastic bags is anything but a feel-good measure targeted at getting their votes.