New York City taxpayer here. Fine with it. 25,000 high-income jobs, even if after 10 years, makes the new engineering campus on Roosevelt Island instantly more productive. Those jobs will pay taxes, spend money in the local economy, and drive demand for East River infrastructure improvements.
I do believe that these sorts of subsidies should be required to be put to a popular vote. Wouldn't be a bad state constitutional amendment, actually...
From the perspective of a city, giving $x so that the HQ gets built there instead of some other city might make sense.
From the perspective of the whole nation, the notion of handing out large amounts of money to gain taxes in location A and lose taxes in location B is clearly ridiculous - let the company pick whatever city is most competitive without the handouts, and if some other city wants that HQ, well, they need to provide better services, not just a discount (which essentially is a loss for the combined coffer of all the governments), unless the gov't "one level up" has considered that it's better for national interests that this area needs to be subsidized above others.
For any single city it may make sense to underbid other cities, but for all cities together it makes sense to cooperate/collude so that underbidding doesn't happen.
City residents generally vote against any new development (literally NIMBYism), so it's pretty likely that this would have been something they're against.
But that it is for specific companies both misses the point of a healthy economy and leads to corruption by definition - not being treated equal under the law.
The problem here is of representation. Ie. the city residents could not agree with their tax money being spent on this.
This is an example where a direct democracy shines, basically any decision which lasts longer than a current politicians' mandate should be voted directly by citizens to align the incentives. Any decisions with effect roughly contained within a voting period could be delegated to 'managers', ie. politicians voted for administration of public things.
The problem today in countries without direct democracy for longer term issues is that they elect these 'managers' to decide on matters vastly exceeding their mandate.