That's not normal, but it is simply what it costs to live in NYC or SF or London. I know tons of people who pay north of $2,500/month for decent (not fancy) apartments in central neighborhoods of those cities. And $3-$4k/month is very common for a single person.
And no, it is not simply what it costs to live in NYC, unless you think you absolutely must live in Manhattan below 96th st. This is like saying the cost of a car is $65,000, because the only car I accept is a BMW X5. Ok, if that is your standard, then yes a car will cost you $65k. But there are cars available for much cheaper, that will fulfill all the important roles that one looks for in a car.