That's a fair criticism, and I regret my tone and making the discussion personal. But as a life-long New Yorker, I do feel a personal stake in all this.
I believe OP is right that the month's free rent offered on an apartment is recouped by the landlord: in the form higher rents, which have become a real problem for many people born and raised in the city and which would likely only be exacerbated by Amazon's setting up shop here, especially under the conditions offered by the city.
Over the past 20 years New York has experienced an influx of wealth without commensurate investment in public services. The MTA is dying, urban blight is spreading and many of the new professional class moving here don't seem bothered by it.
Another piece of "anecdata": walking down Bedford Ave. in Williamsburg a few years back, I heard one wealthy newcomer say to another that she couldn't wait for the local pharmacy across the street from the new Duane Reade to close. Maybe this anecdote doesn't have the force of a "real data" but it may help some people on here understand why New Yorkers aren't thrilled by the prospect of a building a big Amazon campus and welcoming them with a handout.
https://harpers.org/archive/2018/07/the-death-of-new-york-ci...
Unlike the author of this article, I'm not averse to my city changing, but I'd like to imagine something other than the change we've been seeing...