What probably makes the most sense for a business that has N offices plus remote workers who can live pretty much anywhere they want and still do their work is to have N+1 pay scales.
These would be one pay scale at each office for the workers in that office, and one pay scale for all remote workers.
The pay scales for each office would take into account the cost of living in the area of that office.
The pay scale for remote workers would not take into account the cost of living of any particular employee's location.
This is because as far as the company is concerned, "remote" is one location. All that they need to do is pay enough so that they can fill all their remote openings.
That's already how they do things within cities. Cost of living varies considerable from neighborhood to neighborhood in most big cites but do you often see companies having different pay scales on a per neighborhood basis? When I worked at a company in Santa Monica, for instance, I don't think anyone doing the same job with the same experience as me would have gotten very far saying the company needs to pay them more than me because they lived in Beverly Hills and I lived in Pasadena.