Alas it's not really like that. The NYC rental market is incredibly tight. Most places already want a deposit plus first and last months' rent, which really just means double the deposit. Even if you have the cash for yet another deposit on top of that, they often won't entertain the idea. It's easier if you can deal directly with a landlord; agencies will generally have nothing to do with you. That and proof of a job/income should be way more than enough proof, but it's still not.
I'm a capitalist and a bit of a left-leaning libertarian, so I'm not saying landlords shouldn't have the right to act like this, or that I think the government needs to step in and regulate it. If I owned a property, I wouldn't want the government telling me whom I can rent to (more than they already do). Just providing examples of the creeping social credit system we have. I don't think it's about financial security once you're already asking for three months' rent just to move in; the financial part is pretty well covered by then.