"that means double-pressing the home button or side button, authenticating with Touch ID or Face ID, and holding the iPhone near the card reader."
I have used ApplePay in London with both my iPhone X and my Apple Watch, and your flow is somewhat off. One does not wait until one gets to the turnstile to authenticate, one pre-authenticates (pressing the side button twice and authenticates with one's face for the X), and then one has a fair amount of time to get to the turnstile and present the iPhone or Apple Watch to the reader.
It will be slower for people who are not used to it, just as it is slower for people who are not used to Oyster cards. For people who have done it more than two or three times, it is routine and just as fast.
If there's any kind of delay, like having to satisfy FaceID or wait for TouchID, it's going to slow things down and people will get pissed. Nevermind that TouchID doesn't work with gloves on and NYC has winter, and FaceID doesn't always read correctly.
Tourists cause delays, using the current metro cards and Oyster cards in London. Regular riders are just as fast with iPhones.
If I were a New Yorker I wouldn't bother with using my phone and just get the Contactless MetroCard equivalent they're no doubt going to offer.
All my friends in London switched from their Oyster cards to the phones (Android or iPhones) and/or Apple Watches. No need to worry about reloading the card, no need to cary something extra, nothing else to lose, etc.
All the same benefits that tap to pay offers overall.