Well you cant just get rid of Gasoline in the refinery process. Crude oil essentially gets destilled. The different fractions are split based on boiling point/weight. Heavy fuel oil-> Diesel-> Kerosene->Gasoline-> Naphta-> Propane/Butane whatever. That is why making new Plastic is so incredibly cheap. You need (i think) ethylene to make plastic. Ethylene is a byproduct of oil refining. If no one buys it, the whole refinery grinds to a halt because you are not allowed to burn it anymore. They practically give this stuff away. Same thing would happen to gasoline. If fewer people need Gasoline, it will become crazy cheap since you cant really do anything with it, except burn it. So it really isnt that easy. IF you get rid of Diesel/Gasoline you will also get rid of the entire petrochemical industry.Elastomers, plastics, lubricants. A huge lot depends on the sweet dino juice.
Plastic isn't a single material. Some plastic materials (e.g PE, polyethylene or PVC, polyvinyl chlorine, but also others that use ethylene derivatives as intermediates) require ethylene, but there certainly are plastic materials which are produced without any involvement of ethylene or other petrolium derivatives.