Lowering salary costs is one reason. The other potential reason is to vastly increase the talent pool.
If it's only about the first reason then management will cut salaries as deep as possible, if it's only about the second then they'll keep salaries at the same level and just change the job description. I suspect for most companies final pay scales depend on the weighting of two reasons. A lot of companies will try to have their cake and eat it too with location-based pay, but that approach will neuter the benefits of opening up for remote work, and its efficacy will only degrade further over time.
If it's only about the first reason then management will cut salaries as deep as possible, if it's only about the second then they'll keep salaries at the same level and just change the job description. I suspect for most companies final pay scales depend on the weighting of two reasons. A lot of companies will try to have their cake and eat it too with location-based pay, but that approach will neuter the benefits of opening up for remote work, and its efficacy will only degrade further over time.