Because ultimately you have less bargaining power?

Besides, your alternative isn't making more money. It's not getting the job.

If it’s bargaining power, then it’s a power dynamic that may merit being called out, just like gaps in pay by other characteristics.

Some of those characteristics were given protection in law after enough noise was made.

Of course pay is about bargaining power. How do you think a salary negotiation works? Why do you think a software engineer gets paid more than a nurse in most places?

Yeah this is an insane line of thought. You won’t fix pay, you’ll just see jobs stop existing by going this route. Market dynamics in labor are a good thing and you can change your location to benefit from them.

Don't know why the company wouldn't give you a raise for increased cost of living? Plenty of companies will adjust pay based on location, including moving around. And plenty of companies adjust for inflation as well.

Of course any adjustment in pay needs to fit budget, so the company and line manager would need to have the budget to afford to. And there's probably plenty of companies that won't have this as an option or won't adjust for inflation, but there's also plenty of examples that do.

Your salary is a negotiation. Your company wants to pay each employee as little as possible. If you are unhappy with your salary you should look somewhere else. In fact, that is why companies pay people in expensive areas more. Those expensive areas have more available jobs so employees are more likely to leave. If you want those employees to stay you need to pay them more than employees who have a harder time leaving.