In fact, the whole idea of the taxi bargain is that you pay a fixed price to get a minimum standard of quality --- enforcing the minimum standard seems likely to be a more productive avenue than increasing the average.
A more direct solution might be an app that submits complaints to the Taxi & Limo Comm'n, since the fear of losing a medallion is far greater motivator to most taxi drivers than the prospect of being named on an awards list. (Again, for Uber and similar systems, reviews do matter to drivers because consumers choose.)