Public resources in NYC are already allocated by private companies; that's a big part of why local government can't be trusted in the first place. Amazon is just saying that if they build a huge building in NYC, then they want to control public resource allocation in the area of the building in place of whatever private company would already be doing this.
> Where's the guarantee (or even suggestion) that Amazon would use their tax break to improve local infrastructure?
That's literally that the deal is, or at least a substantial portion of it:
https://www.bizjournals.com/newyork/news/2018/11/13/heres-wh...
Nelson Rockefeller smashed heads to rid New York of Robert Moses' strangehold and fix the subways. The Carnegies and the Vanderbilts founded universities. After the '80s we haven't really seen this kind of behavior, save Microsoft's recent tiptoe into developing affordable housing.
Google and Facebook have the weight to throw around to ask for things like the second Transbay Tube or Dumbarton Bridge rail service, but I wouldn't hold my breath.
It's fairly incomprehensible to me - these companies are working with a truly staggering amount of money, do they think they've found the upper limit of "Bay Area Coolness Factor?" Imagine if they eradicated the draw of Austin or New York or Portland by pushing for such a good Caltrain system that living in Mountain View was functionally equivalent to living in San Francisco because the trains were so fast and ran all night... or even further south or east, stretching transit out to areas where one might actually be able to afford a house.