The obvious answer is what is commonly called the inertia of dead ideas. Leaders grow up in one era but take power in the next era and they often bring along with them ideas that are 20 years out of date. Military historians joke “generals are always ready to fight the last war” and political leaders make mistakes of the same category. Offering billions in tax breaks to lure businesses is the kind of thing New York might have sensibly done in the 1980s when they were desperate to replace the loss of the textile industry. Such a strategy makes no sense in 2019, when an abundance of investment has clearly replaced the lost industries.

Because it made them look like they were doing their jobs by making a big, important deal? These are politicians we're talking about

For the same reason that politicians support objectively terrible deals for sports stadiums: their incentives are misaligned. They get all of the positive press when the deal is signed and someone else will have to deal with the long term fallout.

Corruption and wanting to meet a billionaire? Same reason politicians build stadiums for sports teams.

You're getting downvoted, but I don't think it's an unreasonable theory. Cuomo might run for President at some point; having Bezos happy and throwing a million or two into a PAC wouldn't be a downside for him.

Because they were bad politicians?