I'm not so in-the-know w/rt pay: are there a lot of companies that _don't_ do regional pay?
So in practice, yes, but companies aren’t so deliberate about it as to have it in policy.
Depending on the company sometimes the differences in base salary will be very minimal, say $225k in Ohio versus $250k in SF.
An engineer that started on-site with regional pay that now went remote does not equal “we’re a company that hires remote worldwide and we don’t adjust to regional salaries”.
A good example would be a company that hires new staff in multiple countries and continents that pays everyone regardless of their location.