They bring you business. Yes, it helps you that the taxi can have a phone with lyft in the same car. It gives the illusion of choice and it gives an alternative to the driver.
In the end, your business has 90% market share. It's not going away overnight. Market share is actually self sustaining and it's giving you a strong edge for the future.
Competitors don't have 1/10th of the cash. If they get try to compete on subsidies, they'll get a peak of traffic and run out.
"Sell at a loss but make it up in volume" probably doesn't work well for many :)
The bigger thing, though, is that you keep implying that I said Lyft was somehow in a better spot. Now you're noting I never mentioned Lyft.
Nothing I'm saying is affected one way or other by Lyft. Pointing out that they have the same problem doesn't change the rationale.
Self driving cars are just hype that won't be any significant for another decade. You should forget about self driving cars.
What Uber has right now is real, a massive customer base and network of taxi, that is bringing billions of dollars. They could totally focus on that and have a strong and sustainable business.