Well, except that it is. It's an attempt to keep all rent within everyone's "ability to pay" - it's not individually tailored to your particular income, but the idea is that it keeps housing within any given person's particular means. It's socialism the same way that any price ceiling is socialism - you gave the reason it came about yourself. It was instituted to keep the greedy capitalist exploiters from expropriating the wages of the proletariat. Well, not in so many words, but that's what it boils down to.
And it has the same effect as price ceilings have in all other markets - when you artificially cap prices, you artificially restrict supply. In the short term, prices are kept down, but in the long term, the problem is never fixed because there's no incentive to build new property and increase supply.
NYC is full of all sorts of social engineering laws that have all kinds of unforseen effects.