Last time I was in Manhattan was 6 years ago, but at the time an Uber was as-good-or-better than the train for a lot of within-Manhattan trips. I splurged on a bunch of Ubers since it let me see a lot more of the city at ground level, which was fun, and then quickly noticed that when you factored transfers and walking to/from stations, it was no inconvenience either.

Obviously it wouldn't scale that well for everybody but I wouldn't be surprised to see, if self driving cars master Manhattan, some more well-off people who aren't currently at "private driver" level of rich to move to self-driving cabs or such to avoid crowding and go point-to-point.

The big advantage of the trains was in leaving Manhattan and going to Long Island, though, compared to the car-bottleneck-hell of the bridges and tunnels.