That is, you are going to be locked into working for Amazon to maintain your income level.
Not everyone is that mercenary about optimizing their income.
Amazon's hiring pool would be limited to midwestern Universities (e.g. Ohio State) + people looking to reduce their cost of living while working for Amazon + some people that prefer the scenery. Less people are optimizing purely based on compensation - CoL than you think.
To me, that's why these locales were never really in the running. I'm a native midwesterner and I feel bad for anyone trying to recruit a national audience for a midwestern role. You have to have really good sales skills.
SDE's in Detroit, Madison, and Twin Cities are paid exactly the same as the SDEs in Seattle.
Even smaller firms are giving away jobs for 150k salary for just a couple years of experience.