On the current market with human drivers, there are some odd incentives to the contrary though. Using driver-provided vehicles probably helps make the "they're independent contractors" legal argument. There's also the storage yard problem-- if you own a fleet, you're going to have to provide a place for the drivers to come to, park their own cars, and get into yours. I also suspect it lets them cast off the "unknown unknowns" -- damage and insurance claims, underpriced routes. And yes, there are likely opportunities to exploit new recruits by paying below their actual costs.
Once you have self-driving, many of those incentives vanish. Your biggest win comes from calling up GM and ordering cars 10,000 at a time, which a new-to-market entrant can't afford to do.