Above some threshold, which can still be very low, they are going to get massive amounts of tax revenue, aside from the fact that wages, jobs, and citizens paying taxes will increase.
You might dispute this, but I don't see any numbers or qualifiers with anyone saying "tax breaks", in and of themselves are always on balance, whatever the specific details, worse than not having the companies be there.
There are lots of debates on the correct form of taxes anyways. Corporate taxes of non-trivial rates seem pointless to me, or.. detrimental actually. Property tax abatements? No different from a landlord giving rent deferrals to a whale tenant. It can be a very practical choice
Politicians' incentives not being aligned with long term goals of a city? Yes.. that is a problem. But still. The right choice could very well be massive tax breaks, even among those of differing political philosophies.
I sort of agree only on corporate tax breaks - pragmatically there is little point keeping them so high that most international corporations keep their profits offshore. I'd favor lowering corporate overseas rates, but only in combination with increased enforcement against tax avoidance schemes. But to me thats an unrelated to local city/state tax breaks given to corporations.
Since Amazon uniquely doesn't earn much profit, preferring to invest / spend as much of their revenue as possible, one could argue that there is an opportunity cost to collecting more money from Amazon in taxes vs leaving it to them to spend how they see fit. The cost is whatever alternative use they would place on that money... more employees hired, higher wages / benefits, more R&D, more capital expenditure, more construction, who knows.
Or course, in every one of those cases, there would likely be taxes involved anyways...