For me, this starts with my complete distrust of metered taxi pricing in the first place. Literally every taxi ride I've ever had in the States had the driver take a longer route than they could have just gotten from Google, sometimes to the point of absurdity.
With Uber and Lyft, on the other hand, I know ahead of time what I'll be paying.
Drivers are eventually going to follow pretty closely what the metering algorithm wants them to, with a moderate adjustment for passenger satisfaction for the sake of tips. Consider different per fare starting fees, and different per mile and per minutes additional fees. If the fixed revenue part is relatively high you'll end up with very fast, but probably unsafe, cab rides. High per mile rates and you'll possibly end up on unecessary freeway legs. High per minute rates and you might get dropped where there are a lot of new fares rather than where you want to go.
With Uber and Lyft, on the other hand, I know ahead of time what I'll be paying.