Except it won't, exactly because landlords are rational actors. Let's say the upkeep for a space is $400/mo, and the rental for that same space is 3000/mo. A storefront could be vacant for 2 years and a landlord would still turn a hefty profit if they were able to get someone to sign a one-year lease after the 2 years of vacancy.
NYC is a big place- for every 30000 people that think that the rent is unreasonable, there's 1 person who thinks that it is, and landlords only need that 1 person. Renters have no leverage here.
Renters do have leverage here. You're not going to get it for $1000, but you might for $2500 or $2200.
https://www.brickunderground.com/rent/why-landlords-leave-ap...
Trust me, as a resident, this phenomenon is real. There are a number of stores in my neighborhood that have been vacant for literally the entire time I've lived in the area (~ 2 years).
As a general rule of thumb, renters (both commercial and residential) really don't have much leverage in NYC, except under extremely rare circumstances. It's hard to understand unless you actually live here, but the rule governing real estate elsewhere in the USA don't really apply here.
There is so much cash floating around the high end of the economy, thanks to QE and tax dodging and everything you've heard about, that RE is purchased simply as a way to diversify holdings beyond stocks & bonds. It never has to be used.