Remote work – global rate or local cost of living?

How do fully-remote companies set their pay scales? Two possibilities are:

a) Global rate for the role, based on skills and experience, totally independent of worker location. If the worker moves, the pay stays the same.

b) Role-based scales are normalized to a Cost of Living (CoL) index at the worker's location. If the worker moves, the pay changes.

I am interested in factual reports on which companies use which policies, but also a discussion about which one seems the most fair.

It is said that "Silicon Valley startups are a mechanism for nerds to work very hard to pass huge quantities of money from VCs to landlords."

Localized pay seems to subsidize and perpetuate entrenched CoL differences.

Global rates seem to encourage geographical dispersion, CoL equalization, and reward talent in low CoL regions of the world.