Rent deregulation, believe it or not, raises market rate rents. The conservative Manhattan Institute, in their study of deregulation in Boston, showed that, following deregulation, landlords invested in improvements to attract market-rate renters. Landlords always seek their highest rent that the renter is willing to pay. Where there is any competition, the result of deregulation is better quality housing but higher market rents.
Market rates only go down if demand goes down -- if people leave the city or excess housing is built. Rent regulation in NY doesn't hinder construction -- new units are typically unregulated anyway. And the city's population increases, not decreases. It's not even certain that in a tight market like NY, landlords would even invest widely in improvements.
Regulated rents actually help to depress market rates, although renters who pay exorbitant rents wish it weren't so. We'd all like to be able to blame the regulated renters because it seems so unfair. But the source of exorbitant rents is not regulation, but the profit motive of landlords and NYers' own desire to live here -- we are the market that sustains those rents.
The market value depends on three general factors: demand, supply, and the aggregate available funds for rents. If regulated renters are paying less than their available rent funds (the excess of which presumably goes into the goods and services economy), when they are forced to pay more, they will increase the aggregate funds available for rents, since most of those renters are tied to the metropolitan area by work or family. Once deregulated, they will raise rents wherever they go in the area and that trickles up to the luxury rents.
Paul Krugman some years ago blamed regulation on San Francisco's tight rental market. He was clearly unaware that inclusionary housing was mandated in San Francisco, hindering construction. Krugman admits in his article that his judgment was cursory and immediate and not a result of any investigation. Had he known that inclusionary housing was mandated there, he would no doubt have come to a very different conclusion.
Inclusionary housing is not mandatory in NYC. I hasten to add that mandatory inclusionary housing in a super-high market like NYC would probably not unduly hinder construction.