It's not a matter of
need. If you get more companies there is more local demand for labor, which means more jobs and higher wages, which means more tax revenue. Giving a company that will bring in a billion dollars in new tax revenue half that much in incentives still nets you half a billion dollars.
The real issue is that this is true of everything. Cities compete with each other, but major metro hubs have such an intrinsic advantage that it allows them to suffer a large amount of corruption and waste and still not be uncompetitive. Until you're negotiating with a company large enough to bring with it its own economies of scale, and then it does make you uncompetitive, because Amazon could build HQ2 in the middle of the desert and a town would spring up around it regardless, in a way that a guy operating a food truck absolutely could not.
They don't actually want to do that because NYC still has its intrinsic advantages, but if it also has very high taxes which then go to waste and not toward providing useful services, the benefits have to be weighed against the costs. (And realistically there are also better alternatives like Virginia rather than literally the middle of the desert.)
Then the city becomes concerned that their high taxes and low efficiency are costing them Amazon so they come up with some kind of carve outs which they would need to keep Amazon but not the food truck or the real estate developer or doctor's office, and so it applies only to huge corporations and not to everybody else.
Which then creates an unfair advantage for major companies with that kind of leverage, and then they start eating everything and driving out small and medium businesses who can't compete when they're the only ones paying high taxes. And that's what makes people upset.
But you're never going to get Amazon if your offer is to tax them heavily and then waste the money. The way to be competitive on a level playing field is to cut out the waste in general so that nobody has to pay high taxes for low benefits.