Honestly, because it's a race to the bottom. On top of that, there have been many instances of companies negotiating massive tax breaks only to relocate again after a few years.

Those tax dollars are better spent making the city more attractive to people and improving the universities. This will provide for more organic growth through startups founded by people anchored to the city by their social network.

I could see why a city wouldn't want to pay real money and then have the company move, but what's the problem if they agreed not to tax Amazon and then Amazon relocates?

The key here is that the incentives appear to be for a certain company and are not fairly applicable to all companies. Giving those with the best economy of scale yet another advantage. People are often against unfair advantage.