Does the market allow them to pay an employee less because he moved elsewhere?

Honestly, yes, because the number of FT remote jobs is not high, jobs are harder for FT remote people to find and land, and you are actually now closer to competing with offshore options, often augmenting an in-office team.

Remote employers only compete against local employers so yes.

Conversely, if more employers start hiring remote, we will have remote employers competing against other remote employers, which will increase compensation. And this is the reason I’m vehemently pro-remote.

People fear loss more than they welcome gain. There is a lot of demand for good engineering talent and there just aren’t enough engineers with these skills. While many people fear that remote would decrease salaries in high col areas, I believe the opposite will happen.

Of course the second order effects are somewhat difficult to predict. If you can get SF salaries in eg Ohio, it might reduce the number of people flocking to SF reducing the talent pool.