Cost of living is wildly different in different areas. People in NYC need to earn more money than somebody in Idaho Falls to live even close to a comparable lifestyle. A million dollars will buy you an "ok" 2 bed room apartment in Manhattan in an "ok" neighborhood, while a million dollars near Houston will buy you multiple acres with a brand new 7 thousand sq foot 6 bedroom 9 bath home on the waterfront with a guest house and a swimming pool next to a pro-level 18 hole golf course.
If you don't understand it further, feel free to take the midwest salary and try and live in San Francisco or NYC.
OK, but imagine this situation: I have affixed a monitor with a webcam to a robot that represents "me" in an office. It is able to sit at a desk, attend meetings, etc. I work from home in some place with a lower cost of living and use the robot proxy for interaction with my peers. Should I be paid more or less than other people working in that same office, producing the same output?
Less, because those people have to live there where it's more expensive. While you live where you live where it is less expensive.
You're thinking of this as advantaging you, getting SF pay for working in Idaho Falls, but you need to think of is that salary in Idaho Falls is the "normal" base salary, everybody earns at that rate, and cost of living adjustments are paid on top of that base salary for people in expensive areas to create as equal of living conditions as possible in more expensive areas.
This is so commonly understood that nobody bothers to break it out that way except for the Federal Government pay scale. Everybody from Podunk, Nowhere gets excited when they get a job in the big city because of this pay differential on what they'd make where they live. Except the cost differential is similar and when they arrive they suddenly realize it doesn't buy them anything more.
By paying people "the same" at the base salary, your salary model would disadvantage people working and living in cities such that they could not do it and companies that need to be in cities would be unable to function.
Companies with large workforces in cheaper areas could also not pay their workers SF/NYC salaries or their costs would simply overcome their revenue or if they can manage it, they may as well have just hired in SF/NYC in the first place and realized better efficiencies of physically working together. Your robot is a poor substitute for actual face-to-face interaction and introduces lots of inefficiencies into communication.
Not all jobs for a company need to be in the expensive areas, so it would make more sense for companies to push those jobs to cheaper areas. But some jobs do need to be in expensive areas for efficiency. Cities exist because of those efficiencies. However, being a city with 5x population of Idaho Falls doesn't mean you have 5x the resources, so demand drives up the cost of goods and thus the cost of services rise and thus it simply costs more to live there.
Companies wish to continue operating, so they need people to be able to afford to live near where the company needs to be (which is dictated by the efficiencies of the city). This is reflected by pay differentials for people that need to live and work in these cities. Nobody can live in SF or NYC on Idaho Falls pay.
For a variety of reasons, your personal, physical presence in an industry cluster[0] is valuable. Managing a business is a coordination problem, and it's generally the case that said coordination problem is best solved by having everyone in the same office. So an employee in Silicon Valley or NYC is, on aggregate, significantly more productive than the same worker in most of the Midwest, even if their individual effort is no different.
Unfortunately, the dominant housing policy regime of restrictive single-family zoning and auto-oriented transportation, which significantly limits new housing production in the most productive areas of the US, causes high wages and growing populations to lead to lead to extraordinarily expensive, overcrowded housing.
If you don't understand it further, feel free to take the midwest salary and try and live in San Francisco or NYC.