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.