One difference would be that Uber wouldn't be taking a 20% cut of the money involved. That 20% is what people believe pays for the benefits Uber ought to be providing.
I not sure that's true. The equilibrium price could actually be higher than where the market rate is now. Uber, Lyft, etc are subsidising their products with massive amounts of venture money in order to increase their market share - if they were removed from the equation it's entirely possible that drivers would get a higher fare and the cut Uber takes.
Isn't that having it both ways? Either Uber takes a 20% cut, or it's taking less than that to lower fares. I don't have facts, but I don't think Uber is paying its drivers more than the fares it collects over a significant period of time in established markets.