No, they didn't.

Amazon launched a long process, deliberately designed the process to extract the largest amount of tax breaks, took bids from lots of cities but, shortly after, it leaked that they were very likely going to pick New York, Virginia, or Dallas (and, ofc, they picked NY, there was outrage, and they then picked Virginia...which had offered one of the lowest packages, and expanded in Washington DC which was also one of the lowest). The biggest packages, even bigger than NY which offers big packages, were from Chicago, Atlanta, and Pittsburgh...they weren't considered credible at any stage.

The biggest issue was, surprise surprise, supply: not every city that submitted a bid had enough developers, not every city had enough housing, crime was an issue in some places, etc.

Btw, they did start moving out of Seattle because of tax...but it was actually mostly politics. The head tax would only have raised a few mil but it was the fact that was part of a general hostility towards enterprise: no housing, crime, etc. Hopefully, the parallels are obvious to you.