To take a "stab" at it I did some rough calculations comparing (a) the extra income taxes that Virginia and New York will collect assuming 25,000 employees at both HQ2 and HQ3 to (b) the reported tax breaks. My calculations say that it will take nearly 4 years for Virginia and nearly 6 years for New York to recoup the tax breaks via income taxes. Call these "number of years to recoup" (Y). Such simple assumptions likely under-estimate Y.
The above assumed all the new Amazon employees will come from out-of-state, and they will all be added immediately. Both are obviously false. So let's assume that only half of the employees will come from out-of-state and the average number of employees over the first several years will be about half of the numbers shown above. Adjusting for both of these factors implies that Y will be nearly 16 years for Virginia and nearly 24 years for New York!
Arguably Y could be reduced some for favorable side effects like income to local businesses and rents. On the other hand, there will be unfavorable side effects. The presence of HQ2 and HQ3 will increase other costs to local people for things such as paying more for teachers, food, rent, infrastructure, and so forth. These are, of course, very difficult to quantify. But if the net effects were to reduce Y 1/8th, the result is still nearly 14 years for Virginia and nearly 21 years for New York! I'm inclined to agree with the professors.
I am confident that not many people in the general public do the above kind of analysis. Therefore, politicians can hand out tax breaks to Amazon or whoever, and most people in the affected community will swallow whole whatever the politicians say about it being a great deal for the local economy. Even if some of the people are skeptical about how good a deal it is for the community, there is little or nothing they can do once the tax breaks have been finalized.