Earning (made up numbers because I don't even live in the USA and I don't know what is reasonable) $100k and spending half of it on rent with no hope of buying a house is still better than earning $50k in an area with much cheaper housing.
Of course if you can score a remote job then you can have the best of both worlds, but that isn't always possible (and some companies seem to pay differently based on your COL now).
However, today’s high inflation rates make all these computations iffy, and if you rely too much on inflation beating stock market returns, you won’t be able to ratchet down on risk as you get closer to your preferred early retirement date (a crash can dump you back in the workforce at a bad time). Also, many people in HCOLs don’t want to downgrade to LCOLs after they retire.
Too bad Medicare doesn’t transfer to low cost but nice southeast Asian countries.
Desirable places to retire like Santa Fe are already getting expensive.
Cheap private healthcare works for small things, but you are paying out of pocket for everything and if something big comes up you might not even be able to access the care you need. Guam might work instead, but they aren’t cheap and are pretty far away from anything.
Sorry, having lived in Mississippi for 4 years, that is not really true. Or I guess it depends on what you mean by "many", because there are many bad cheap places out there (e.g. Gary Indiana, Port Gibson Mississippi, Monroe Louisiana, ...). It also depends on what you mean by upgrade: many people like big city amenities (food and cultural options) and would see moving to the sticks as depressing, just like many would see the opposite (they love the country side, hate big cities).
Internationally, LCOL areas are generally in developing countries, and even a city like Bangkok will get expensive after awhile (though big cities in the west might get more expensive faster). It is still a trade off, many can't make (and many can, good for them).
If you have a high salary, you are probably living in a HCOL area.
If you have a low salary for the same kind of work, then you are probably living in a LCOL area.
The savings rates of these different individuals could be the same if the salary difference is proportional to the cost of living difference.