I wouldn't have a problem if Uber allowed riders to select a default tip percentage for each type of service. I travel a lot internationally and I like not having to convert money as soon as I arrive at the airport. Since cell service can be spotty and occasionally expensive, I use Wi-Fi at the airport to book a car. Until I arrive at my hotel, I couldn't easily add a tip to my fare even if it was part of the app.
In NYC, for non-surge rides depending on travel speed without tipping Uber may be more or less than taxis. Uber might need to cut prices if tipping becomes the norm in NYC to remain competitive with taxis.
For rides from Westchester and Fairfield counties to NYC airports, at current rates and a 20% tip I don't see a compelling reason to take Uber instead of a car service. If there is no traffic and no surge pricing, I believe Uber will be less. If surge pricing is in effect or traffic is moving slowly, Uber may cost considerably more than a car service that offers a fixed rate. With a car service, I can select the time of pickup and I know what the ride will cost in advance. I don't have to worry about surge pricing, driver cancellations or traffic.
My guess is that Uber prices reflect what Uber believes is necessary to attract riders. If tipping becomes the norm, it is quite possible that prices will go down and drivers may not end up better off even if everyone tips generously. Some people check Uber instead of Lyft because they believe that Uber's all in price is cheaper than Lyft's and only check Lyft is surge pricing is in effect.