I mean, "poor" might mean different things to different people. Call it working class? I'd rather commute from the Bronx for $2.90 than from Croydon (in many ways the Bronx of London) for, like, $7. I'd much rather get heating for free than pay, like, $5k in London.
If you're on the street, none of this helps you much, but across many metrics, I think NYC might legitimately be more affordable to live for the working class than London or Paris.
i don't know enough to comment on the cost of "normal" living, but think about what happens in NYC the moment you get laid off or, even worse, get sick. I think at that point Paris starts becoming a lot more attractive if you're working class..