If a remote-first company can give someone in a nearby time zone with the same language and cultural background and the same skillset a tempting offer while saving themselves 25% of their salary band, they're going to do it. It's not because they think you're less productive, it's because they're now looking in a wider job market with more competition from people who need less money to live.
The converse is also true: if you're living in a low CoL area, WFH can actually bring you a huge pay increase, because salaries balance out somewhere in the middle.
(I'll add that I strongly believe that where you live should not impact your income if you're in a remote company, for the reasons you list: if you're in the same country as everyone else, your location of residency has no impact on your value to the company.)