Currently Lyft (haven't used uber in ages but I assume they do the same) gives an exact price as you're selecting a destination before you're assigned a driver,

Currently Lyft (haven't used uber in ages but I assume they do the same) gives an exact price as you're selecting a destination before you're assigned a driver, to allow driver price negotiation you can't give an accurate price before a driver accepts. At best you could give the driver more of the company cut but Uber is already lighting mountains of cash on fire as it is to increase driver income.