At the end of the day a lot of this seems like sort of an accounting question.
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...
We do know. Taxes are already fairly low in the US. Kansas ran a broad scale experiment with dramatically lowering state taxes - the results indicate that some magic growth is not unlocked. My conclusion is that cities are just giving up local budget balance for little benefit.
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.