Look, a set of policies is not the same thing as a school of thought. If you open any microeconomics textbook, you're probably not even going to find the phrase anywhere in the text. There is no "supply-side" theory of consumption, inflation, etc. Surely you know the difference.
The schools of though associated with those thinkers isn't "supply side". Mises/Rothbard represent their own strands of Austrian economics, Hayek was a mixture of Misean and Classical economic thought, and Friedman started out as a Keynesian that later ended up levying some pretty significant critiques against Keynes (referred to as Monetarism).
I realize that this might seem pedantic, but the idea that "supply-side economics" represents a dominant school of thought in academic economics isn't realistic at all, and it's largely a result of misinformation (from left and right-wing groups). As someone who corresponds with actual economists, I've never actually heard the phrase being used by one.