Price sensitivity doesn't depend on every user obsessively tracking prices.
If Lyft becomes a better deal, a vanguard of users notice it, they word of mouth it, and the equilibrium shifts somewhat. Not all the way, there are price insensitive users. But there are also price sensitive ones too.
- I wouldn't even know if Uber raised prices by a dollar.
- I don't price-shop between services.
- Uber is still regarded as "cheap", including vs. taxis.
- Uber's gotten people hooked on on-demand transportation: taxis are dead.
I think there's less price sensitivity than you think. Combine that with the obvious PR move to spin price increases as a way to pay drivers more, and competitors will (have to) follow suit.