I would say that fossil fuels are very important for a lot of our battery technology. I believe that a large number of important chemicals and materials like plastics are derived from oil.
They are important, but not as important as they are to transportation. The quantities of oil required for fuel production dwarf the quantities required for plastics and other important chemicals. It's still a sizeable amount but not even close to what gets burned every day.
It's just that fossil oil is - relatively speaking - very cheap compared to other sources.
