Is there a fair way to adjust based on living costs - within certain bounds - that isn't based on rent index, or at least weighted in favour of lower cost areas? Paying Bay Area salaries for every employee just isn't feasible for most startups.
The only fair way to adjust is based on value to the company, and what the potential employee is willing to accept. It isn't reasonable to use pay to remove the financial advantages of a candidate's choice of location, and then claim "you can now hire the best people on the planet in any particular function" as the original link does. If someone is among the best people on the planet, they'll likely be paid considerably more than the San Francisco average without regard to what their costs are.
One of the touted benefits of working remotely, for those who can, is exactly the ability to trade off the advantages and disadvantages of living in places with varying characteristics, and it's unsettling to have a company which claims to support and encourage remote work also be upfront about actively working against remote workers' ability to make these choices.
AFAICT, the flipside is that "flat global pay" is that then the company can't offer as compelling an offer to those in expensive areas. (i.e. if everyone paid a flat fee and you were stuck in an expensive city, then you would be penalised when looking for remote work).
How does that explain the large number of Bay Area, on-site-only startups?
None of these are perfect, you're never going to get two truly comparable locations when accounting for mortage/rent, groceries, cost of transport, cost of consumer products etc., but it's a whole lot better than mainly looking at one variable (rent).
Not for work where the employer isn't specifying a location constraint. For on-site work, while one can debate the exact ideal formula, location adjustments within a firm based on comprehensive cost-of-living makes quite a lot of sense.