At the company I work for, HR defines pay bands based on the HQ location and there's a % modifier based on where you live. So yes, if you move to a higher COL area, you get paid more. If you move to a lower COL area, you get paid less. Honestly, I thought this was a normal and uncontroversial practice until this.

Frankly, the calculus of your pay probably depends a lot less on your knowledge or output than you seem to think. Geography and luck play as large of a role.