I don’t really think “should” comes up in those discussions. Companies pay as little as they can get away with, restricted by the need to retain talent.

People in higher cost of living areas will probably end up with higher salaries in general because, for a given level of financial wellbeing, they need a higher salary. So they’ll be more incentivized to do more things that result in higher salaries: move jobs, go for promotions, negotiate more, etc.

Companies will try it. Workers will push for arbitrage-free pricing. It's just business as it always was.

I think over time (say the next 5-10 years) there will be upward pressure on remote salaries and eventually they will normalize to being approximately in the same range as the Silicon Valley ones because of economic pressure: everybody is still going to be competing for workers everywhere. The competition is simply going to get bigger as firms realize they can hire top talent from other places and they need to in order to find and keep the best people.

From the lens of the internet as means of disintermediation in society this makes sense. Using this framework to reason about the internet, we might think of different ways that the internet removes barriers to communication; recently there are several social phenomenon where the internet has removed geography as a barrier to communication enabling lots of different social changes. In this framework, salary and employment markets were just slowly going to eventually get geolocation disintermediated. The pandemic has just sped that up 5-10 years. Now instead of taking 10-20 more years it'll take 5-10.

So to your question, I hope not.

https://www.cnbc.com/2019/08/19/stanford-is-no-1-on-our-list...