I've even seen this already happen in real life for distributed companies who already have non-Silicon Valley offices; when someone wants to move to SV and asks for the corresponding fairly massive raise, they've been told "no".
There'll be a honeymoon period where this may be true but this is the inevitable stable point, and we all know it on one level or another.
The only reason this looks even remotely feasible for the companies is the accidental historical fact of them all living in a high-expense area. Once they get more used to a more widespread remote workforce, this policy will only ever work out in the company's favor, never yours. There is NO WAY we're going to have the right to simply announce to our companies one day that of our own free will, we've decided to move to a 30% more expensive place (because why not? they'll pay for it, supposedly) and they'll just give us a 30% (or whatever) raise. Ludicrous nonsense. It's a lie.
If this point isn't a stable point, it'll end up tipping in the other direction... companies pressuring their remote employees to stop living somewhere so expensive and move somewhere cheaper. "Pressuring" here includes things like "when layoffs hit, hit the high-cost-of-living employees first", in addition to direct threats.
Enjoy the remote work honeymoon; it isn't going to last.
I have essentially the same problem in Japan. I mean, big companies usually have offices in Tokyo, but if I want to work for a startup somewhere, it's always going to be contracting. For a variety of reasons, that's sometimes not desirable (and a lot of companies refuse to hire contractors for lots of other reasons).
So, basically, the only way you're likely to run into this is if you move to SF, which is usually no problem ;-)