Why not go back to paper bags? Here are a few reasons:
Making paper is a very polluting process.
Paper bags tear and get wet.
They cost more
They do not biodegrade in landfills where most trash ends up. Nothing does.
Plastic bags are made from natural gas, not oil (polyethylene), and we have more natural gas that we know what to do with.
If we burned our waste, as we really should, we could recover all the BTUs locked in the plastic and paper and turn it into energy.