But anyway, if you follow the logic of the thread, it was: (A) location-based pay is justified because of location-based cost of living --> (B) then is car-based pay justified because of car-based cost of living? --> (C) no, cars are a personal choice --> (D) your car is as much a personal choice as your location; it's only not a personal choice to the extent that your employer pays you to choose in a particular way, so using that reasoning to justify location-based pay is begging the question --> (E) your reply, that location is a personal choice, which is a counter to the claim (C), not to my response (D).
As far as negotiation goes, you might be amazed the extent to which companies are willing to shoot themselves in the foot to stand by their non-negotiable policy. I've seen it. And the calculus is this: you might be so skilled that you're a bargain even at $1 million, but if they pay you that much, it increases the market value of other skilled workers in your area. And if the market discovers this information, that might cost the employer a lot, even though it has nothing to do with you. So they'll tell you you can have the $X you want, but only if you move to a city where other skilled workers are already being paid that much, even though they don't actually care what office you're at, or even if you work remote full-time anyway.
Cost of living doesn't justify location based pay. It happens to correlate, but if a company could offer you an less pay in a high COL area without you declining the offer, then they might. They could even move their entire operation to an area with 1/4 the labor rates, like the Philippines, but there are big reasons they don't.
> then is car-based pay justified
Car based pay doesn't exist AFAIK, so what's the point? Companies pay what they have to pay to hire/retain the employees they want. There are a myriad of factors affecting any labor market, including all sorts of day to day personal costs like housing and transportation, but those are distilled through the personal choice of the employee. The main input to what employers pay is what other employees pay - it's a feedback loop at an unstable local equilibrium.
That said, if a major company or three decided to move to globally uniform compensation (the same pay in Czechia as Chicago), well that would be an interesting experiment to watch, though I wouldn't want to work there.
You still have the personal choice to live in the city of your choice, either by not working for a particular company because they don't offer you the ability to work from your preferred city, or working for the wage they are willing to pay you to work from there.
> it suddenly stops being a personal choice, which justifies the extra pay for living in that city.
I don't think "justification" enters the consideration for extra pay for living in city X or less pay or no job for living in city Y. You are offered a set of terms of employment working from a given place. There is nothing stopping you from attempting to negotiate different terms. Maybe you can improve on those terms. Some people have enough leverage to work from anywhere they want without any pay decrease. Not me, but maybe you!