Why would a boss want to pay you more because you live somewhere expensive, unless living in that place is part of the job description? The only reason I can think of is they believe that you might quit in favor of a local job which pays more, and so they need to raise your pay to remain competitive.

But if they know you're committed to remote work, this wouldn't seem to be a consideration. And presumably the possibility of taking a remote position at a company in a high-cost area exists no matter where you live, so by the same logic you'd think that a boss would want to always pay a rate that's competitive in expensive markets.

I guess the reality is that physical location is still enough of a determiner of job options that it influences what a boss understands your realistic pay range to be. But I wonder how this will change as more tech work becomes remote.