A cooling rack is not a heat sink. It’s a place to put hot things because not all surfaces are heat resistant up to cooking temperatures and not all hot vessels can be dumped on a cold or potentially wet surface.
I don't think it changes the rate of cooling that much, just more of the the heat is transferred by convection to the surrounding air instead of conduction to the surface (which for a stone countertop has a lot of mass to absorb heat making them notorious for blowing up hot glassware on contact).
> free heat that we couldn’t control
I understand the appeal of free. It’s the idea of someone else controlling it that gives me anxiety.