So naive.
In an ideal, utopian world? Maybe it would work this way. Maybe.
In reality, your compensation is a function of your negotiating power. Some people, in fact, manage to get the same pay even when working remote, because they're "highly employable". Others don't.
And let me add: I almost agree that remote work shouldn't necessarily command the same pay. A company's goal is to "extract" from each employee more value than his/her/their salary. If a company manages to save on a salary because the employee doesn't have much negotiating power, good for the company.
This is not to say that a company should do anything it wants, far from it. It simply means that if you accept that you live in a market-enabled society, your salary is at stake, too. You want to pay $2 dollars for milk, instead of $20? That's thanks to competition between companies. That's market forces at play. You want it there? Accept it on salary negotiation too.