My Wells Fargo ATMs give me customized short-cuts, touch-screens, cheque scanning, cash depositing and a bunch of other features. It's not quite as integrated as this, but it's nowhere near the sad state of cash machines in the UK.
I can't think of a situation where I need cash at all, except for a few vending machines. If I need to buy a car or something from an individual, it takes me 5 minutes to transfer the money using the web. If I want, I could even setup a list of friends/family (for safety) and transfer money by sending an SMS message to my bank.
I too live in NYC and live an 80% cashless existence. I typically never carry cash unless I'm hitting a poker game.
I think 90% of our machines are just there to get money, not deposit it, so maybe we had more chance to come up with a streamlined and simplified process.
Most early ATMs gave cash first and there was a significant minority of people who forget their cards. I can't remember the paper, but it's pretty essential to be people first in design, rather than engineering first.