I'm in NYC, and I use taxis 99% of the time because of this phenomenon: Uber/Lyft drivers rapidly accept your ride, then cancel (or slow-play the pickup, so that you cancel, to protect their driver rating) as soon as they see it's a place they don't want to go.
It's so bad here that I just won't deal with Lyft and Uber unless they're throwing serious discounts my way, and I have time to burn.
That really depends on your neighborhood. In the outer burroughs, you can walk some ways before you reach a busy enough street to find cabs.
If you have bags, small children, or are disabled, that walk is basically a non-starter.
I thought the driver couldn't see the destination until they started the ride after you get in. Although I've encountered drivers starting a ride as soon as they see me on the street (which I contested and got money back for).
"Ubers don't want to go to the airport for the same reason that cabs don't."
Yep, or they even just call you and ask you to cancel.