It's going to cost you just as much if I use mine, instead. Expenses, insurance, maintenance, depreciation, plus a fee for use of the vehicle. You can pay it separately or as part of my pay, but it will cost you just as much as leasing a company car. I can't afford to spend my money for your business profits.
There are always “use your car” jobs available. Order pickup and delivery, courier, home health, and many others. One bakery of a national brand wants people to drive around restocking convenience stores in their own cars. Even pizza delivery should provide company cars rather than the junkers you usually see. The only reason not to is to sucker workers into using their own resources for the company's benefit.