Exactly, this was a huge communication error on Amazons and the politicians' side. Offering such huge subsidies to a single company will never go down well in the current political landscape - especially not in a city with a resurgent left.
This is only irrational in a narrow accounting sense, and even then only if you believe in the numbers turning out as purported. You are considering a simple one-time game of "give me this and I'll give you that".
What is the long term effect of having government hand out money to every business that creates a hype? What is the effect of the amount of similar deals that will inevitably get hyped?
Should you play the game at all? Is it reasonable for someone to come along with this kind of deal? Is there no sense of fair play - that all corporations should be treated equally - whose logic is outside of the simple arithmetic?
The simple arithmetic that you are suggesting can potentially lead to unpleasant situations. What if the opposite were to happen? Supposed some big firm like Google decided to ask the government for money, or else they leave and sack every employee who doesn't want to go to their new ___location?
You could have firms queueing up to present you with new math problems.
Subsidies are paid out of tax dollars. Surely you're not arguing that Amazon's 2.5 billion investment will go straight back to the city's coffers?
It would generate property tax (if not abated) and income tax for the workers (both hired after the fact, and hired to complete the construction), but at what percentage of the total investment? 10-20%?