You don't pay a fare to exit the New York City Transit system, so nothing will prevent you from leaving during a fire; control system failure or otherwise. There are also emergency exit doors (that many people open to exit more quickly in normal operation of the subway). One may argue that having to go through a turnstile at all is an evacuation disaster, but presumably the designers thought about this and the exit doors are adequate in an emergency.

This is different than systems like London and Tokyo, where you pay for the distance you traveled, and a station evacuation mandates opening the fare controls to let people exit more quickly. For better or for worse, that option has never existed in New York.

It's been a while...lockdown...so I'm recalling memories from ~ 1 year ago, the last time I used the tube (I live in London), but if I remember right, each gate has a red emergency stop button you can hit to exit in an emergency.

Er. No?

Gate lines in the UK are manned, if there isn't someone available to supervise the gate line, the gates are left open.

There is no "red emergency stop button" on the gates. Perhaps if the maintenance controls are open there's a red button inside somewhere, but that's not what it's for. Most likely you're remembering other emergency stop buttons you saw, e.g. on escalators or in lifts?

There are red emergency open buttons for the gateline operator. Here is where they are, in the London Underground training video for gateline operators.[1]

[1] https://youtu.be/lRdkI09KCpk?t=220

True, but those aren't controls on the gate. I guess I should have mentioned them in my list of other places the grand-parent might have seen red emergency stop buttons.

I must be remembering the escalator ones, that makes more sense.

I think an emergency could also require someone going in, like ambulance crew or firefighters and the likes.

Usually here are gates with a fire alarm next to them so you bypass them when needed.