Very little oil is used to make plastic.
In Europe between 4–6% of oil and gas is used for producing plastics and globally around 6% of global oil is used. By contrast, 87% is used for transport, electricity and heating.
https://www.bpf.co.uk/press/Oil_Consumption.aspx
6% is hardly a small fraction at scale.
6% is hardly a small fraction at scale.