Cost of living adjustments and location-based pay

In discussions I've seen over location-based pay, almost everyone I've seen conflates cost of living adjustments with location-based pay. A typical discussion goes something like this:

A: Why do people living in [some remote location] get paid 40% less? That's not fair to get paid less for the same work.

B: But housing is so expensive in SF! Some of us couldn't afford to live here if we were paid a lot less.

A: But you don't have to live in SF. Why should I get paid less than you because you choose not to live in SF?

B: Some of us can't afford to move or have other reasons for being here. You should respect those preferences and we should be paid enough to live here.

A conversation like that could sort of make sense in a company that did cost of living adjustments for pay, but no major tech company I know of does cost of living adjustments. Instead, the adjustments are "market based", i.e., the company is trying to pay as little as it can in each market, which is why people in London, Hong Kong, and Singapore make less than U.S. remote employees in rural areas despite having a higher cost of living.

Bringing up the idea the idea that the company needs to keep its cost of living adjustment because SF has a high cost of living is irrelevant since the company isn't paying relatively well in SF so that employees can live there comfortable, it just happens that the market in SF is very hot and the market in London is much less hot despite London also being quite expensive!

I view the "cost of living" framing as unfortunate since employees who use it seem to think that the company is "on their side" by keeping pay high in SF, but it's not really "trying to" keep pay high in SF, it's just that it's forced to and people who conflate these two things end up advocating for the minimum "market based" pay everywhere, which is better for employers and worse for employees, while thinking that they're advocating for employees.