One could argue that Uber can offer lower rates by having higher utilisation -- those people who are part time Uber drivers clock on at peak times. However, I think this argument is specious, because most uber drivers are full time.
I would argue that the reputation system for drivers (and passengers) is an improvement over the current taxi system. The online booking system (app) is massively better than any taxi booking system I've used. These are strong incentives.
Obviously taxi systems involve paying the state for a licence to operate, but the ~500k price (depending on location) is solely due to an articficial scarcity. There needs to be some external regulation, so Uber/etc should pay some per trip/km charge.
One of the biggest problems with Uber and Taxis is insurance. Basically this cost/risk is being directly transferred to the driver, who may have no assets. It isn't acceptable for a service like this to have un-covered liabilities.
The other big gap is that Uber and Taxi companies have terrible employment practices. Failure to pay payroll tax is only the tip of the iceberg.