Uber/Lyft did outcompete taxis on merit, and to suggest otherwise is revisionist history! Before ride-sharing apps, the process for getting a taxi was:
1. Stand on a street corner (if you're in a busy area) or make a call if you're not. If you have to make a call, there's a ~20% chance a taxi actually shows up.
2. Get in the taxi, tell your driver where to go and how to get there since they could otherwise take a more expensive and profitable route.
3. When you're at you destination, pay the driver. 80% chance they will say "the machine is not working," offering to take you to an ATM to get cash if needed. Note that the machine magically works when you shrug and tell them you're not obligated to pay if the reader is broken.
Ride-sharing apps completely changed the game. Suddenly you know exactly how much you had to pay, in advance. You knew exactly where your ride was so you had an estimated arrival time. You knew exactly what route they were taking.
People talk about how Uber/Lyft dodged taxi regulation, which is true, but the reason there was so much regulation around taxis in the first place was because the old system was so ripe for abuse. Imagine being a tourist landing at an airport and taking a taxi to your hotel; what if you got into a cab and they charged a hidden $20 "airport pickup fee," or took the scenic route, or simply charged a higher rate than the car in front of them? That's exactly why the industry was so tightly regulated, and you have things like standardized rates, requirements for rates to be displayed on the interior and exterior of every cab, the meter being visible to the rider, etc.
All this to say, any sort of competition on pricing is totally orthogonal to competition on product. Uber and Lyft handily won the product battle against cabs.