"app-based routing" is a mirage anyway. When you request an Uber ride, your request is advertised to drivers in the area, who can choose to accept it. There is no routing happening.

Sure, the driver then drives a route given to them to by the app, but so does everybody else, just in that case, the app is Google Maps.

AFAIK, the only routing cleverness is that the end of a shift, drivers can request to only take passengers who are heading in the direction of their own home. That's useful.

Medallions alone should be enough to make a difference. The efficient use of time probably has much less of an effect on earnings, if true.

I'm also not terribly convinced of this. Medallions are a one-time fixed cost. This should have little to nothing to do with long term prices, especially given that the prices of medallions have gone down significantly.