1) We don't cut down old growth trees to make paper products - we cut down fast-growth trees that are farmed for exactly this purpose. Cutting down these trees is not a problem, and in fact pulls some carbon out of the atmosphere because the trees captured it and the paper product end of life is usually getting buried where the carbon is mostly trapped.
2) You're ignoring that renewable energy can be used for production.
3) You're also ignoring that common plastics start with oil, which isn't just used for making plastic products. If you see a bunch of plastic bottles, you should also be thinking about the other oil products associated with them that got burned and turned into GHG.
Do you honestly think that industry uniformly manages their forestry in an environmentally friendly manner?
You could use renewables but the fact is that most of the input energy into paper mills is natural gas co-generation because you need both heat and electricity.
Petrochemicals are used in 90% of the regular every-day items we live our lives with. Clothing, furniture, our homes, cars, personal belongings… banning single use plastics isn’t going to change that.
I’d rather plastic waste in landfills than more CO2 emissions.
[1] https://www.epa.gov/ghgemissions/sources-greenhouse-gas-emis...
[2] https://www.epa.gov/facts-and-figures-about-materials-waste-...
https://www.ucsusa.org/resources/wood-products#.VxfvaJMrJZ1
On paper recycling:
https://doi.org/10.1038/s41893-020-00624-z
https://www.ucl.ac.uk/news/2020/oct/paper-recycling-must-be-...
This is a strawman: you insist comparing two harmful options and ignoring others.
For example, in many countries own reusable shopping bags made of cotton.
They last a decade and are even more comfortable to carry.
https://qz.com/1585027/when-it-comes-to-climate-change-cotto...
Intuitively, this makes sense to me: cotton comes from a plant that can be harvested and replanted, just like paper. The main difference is that you use a lot more cotton to make a cotton bag.
The former is trapped underground in a location engineered to prevent seepage and runoff, and will be sitting there for a thousand years where it only poses a threat to the bacteria and worms in the landfill.
The latter required a tree to be cut down and used 43x more energy, and therefore it’s waste is in the atmosphere warming our planet.