Except by definition if I'm working remotely the hiring pool is every remote company, plus the local companies. That means the floor on salary is the greater of remote or local.
So in cheap areas you have to pay globally competitive, and in expensive areas you have to beat the locals.
Thus, it never makes sense to reduce pay for someone moving. Your goal should be to keep salaries above that floor, not pay as little as possible.
The remote companies tend not to pay as well as some of the SF and valley firms. It costs less to beat the remote firms than to beat the local competition in the Bay Area.
So in cheap areas you have to pay globally competitive, and in expensive areas you have to beat the locals.
Thus, it never makes sense to reduce pay for someone moving. Your goal should be to keep salaries above that floor, not pay as little as possible.