Isn't that the critical point? Of all our environmental problems, atmospheric CO2 is the biggest one, right? My assumption is that the energy used in industrial manufacturing is almost always non-renewable. If we're advocating for using paper bags over plastic bags, that means we're advocating for way more CO2 in the atmosphere. So what we should actually be advocating for is mandating that people reuse bags, bottles, and containers of all kind.
It's been a long time since I've been involved in chemistry, but my understanding is that extruded polymers like plastic bags, wraps and containers are almost always synthesized from waste products of fossil fuel refinement. If it wasn't for products like plastic wraps and bags, these "waste" gasses that are polymerized into plastics would be released into the atmosphere (especially in places without environment regulation or enforcement). The production of plastics at least traps those gasses into some solid state that we can then hope to maybe possibly bury in a landfill. I know it's ugly and pretty horrible, but from a climate perspective I'd go so far as to say that I'd prefer the plastic in a body of water than in the atmosphere.