If you could pay someone in CapitalCity as much as SmallTown, a business would. It doesnt pay more because of some middle-manager's sense of fairness.

Rather, no one would work for you in CapitalCity at SmallTown salaries.

(One of the reasons is the higher cost of living, but that isnt what keeps the salary high, it's that there's no labour supply at SmallTown salaries.)

This is all a distinction without a difference. Salaries follow the labor market, which follows the cost of living. The cost of living is different in different places, because of differences in the labor market (demand side) or because of geographical reasons (supply side).

It's not, because "location-based" pay will change if the market price of labour at that location changes. Location is a proxy variable; a distinction which makes all the difference, see for example, Detroit

Right, okay. That makes more sense now. Thanks!

Salaries don't just (or even) follow the labour market or the cost of living. They are upper bounded by the value an employer assigns a role, and lower bounded by the price an employee is willing to accept to do a role.

Within those two bounds, labour markets can play, but the cost of living going up doesn't automatically make more salary money available.