I hear you, I'd do exactly the same thing.
IMHO the compression test is helpful, but a good ear on a leak-down can tell you much more about the engine. I've heard stories of mechanics that can pinpoint exactly where the problem is from the sound of the air.
true
air out the exsaust, exssasut valve issue
out the intake manifold, , intake valve issue, into the valve cover and not in water, , head gasket into an oil passage or rings, into the radiator, blown gasket into a water jacket
before we had leak down testers, we just hooked up an air hose to a spark plug fitting, and pumped air into each cylinder, not to exceed normal compression of the car