Guys what you will actually find, apart from the stone damage side of things, is that alot of this stuff develops from tail wheel aircraft. Runups into wind helps you keep directional control on the ground at high power settings. It also helps you plant the tail firmly down.
As for engine cooling, many engines do suffer from heat soaking when on the ground. The reason many flying schools teach into wind is because many of there will not have CHT's and therefore it is really hard to judge your engine temp.... similar as to why schools wait for the oil temp to be in the green arc..... is your cylinder head warm enough? So it is prudent for new pilots to enable as much flow as possible, especially when running those before takeoff checks on the hot days.
As for being airmanship.. well........................................................ ..................................
my two cents