Flat payment scales that don't vary by location and are benchmarked to more expensive areas do exist. [1] But companies that do that certainly aren't typical and I assume are all pretty small--including being in a position to pay well above local market rates for lower cost-of-living areas (and/or putting up with a much-reduced ability to hire in high CoL areas).

[1] https://m.signalvnoise.com/how-we-pay-people-at-basecamp/