Having been an Uber /Lyft driver I can't even fathom what it would mean for a driver to be an employee with expenses paid. Is the driver driving a gas guzzling F250 entitled to a higher reimbursement for cost of driving than me driving a Honda insight?
I think the default is the government reimbursement rate. This year it's $0.58/mi. When I worked at a pizza place in high school drivers were reimbursed at this rate. That's a similar market because pizza delivery drivers drive their personal vehicles and it doesn't matter if you drive a Prius or a Hummer.
Professional drivers already exist. Look at any taxi, delivery, bus or transit company. That's what Uber would do. Lease a bunch of vehicles and tell people to drive them for 8 hours a day for a flat rate, and they'll have strict hours and no flexibility.