If high COL located companies starting going fully remote, it's a huge opportunity for workers in medium or low COL. For workers still determined to live in a high COL, it will absolutely put downward pressure on their salary. Their labor market is being exposed to a lot of competition that wasn't there before.
I think if this trend of going fully remote holds up, it becomes much harder to justify living in an expensive city, especially as workers age.
There's still distinct benefits to big cities. You can order stuff online fast, even groceries. You get good Internet connectivity, which is a thing that you need for remote work. Lots of services around.
Define “big city.” I live in a medium-sized city in a low cost of living area and my house has AT&T Fiber, Google Fiber, and cable available to it. I dare say that’s better than most people in the Bay Area have access to. And yes, Amazon delivers here too.
I'm sure that the reduction of CoL opens up plenty of financial room for a car, but it's a whole extra set of things to have to worry about that I personally would rather not.
Further corollary: more workers will be concentrated around 2nd-tier hubs where their wages will be lower than 1st-tier, but higher that median wages. 2nd-tier median wages will then drive up housing prices which will rinse & repeat COL increase trends seen in the Bay Area.
Hopefully these other hubs will have better development zoning & housing policies than San Francisco / Bay Area.