This gets in the way of the "economic" solution
@Destroy: I completely agree.
Having the market set the price is exactly what makes this cheap in boring time periods, and then expensive but balanced in busy time periods. If some disaster happened (like terrorism, or a transit strike) then you would expect the prices to go sky-high initially, and those prices would motivate people to become suppliers, driving prices back down or at least dampening the increase. There would be a new equilibrium point, albeit at higher prices. And that would be right at the time that you needed the transport capacity the most. It costs the city practically nothing to add transit capacity via Uber (especially when compared to adding buses or trains.)
So with this price ceiling, all it will do is create scarcity as demand goes up but supply remains. Or people may even withdraw from the system so they can be completely independent. Nice job. Right exactly when you would want to have a fluid market for transport.