The results aren't theoretically perfect, like applications of aerodynamic rarely are, but power changes in conventional airplanes are very heavily weighted towards a single output. So much so that it's a valuable principle to fly by, in my opinion.
Not really.
Try getting in a Cessna 172, trimming for level flight at 80 KIAS, and then yanking the power to idle. Watch the airspeed. It won't be close to constant. It will go
up. Quite a bit, since you've removed all the propwash over the elevator, reducing its authority.
It will probably work a bit better with a T-tail.
Some airplanes have props well off the centerline, so you get a big pitch moment from throttle changes. An example is a Lake Buccanneer, which has a very high propeller to keep it out of the water. Pulling the prop pitches
up and you
lose airspeed, the opposite direction from a 172. Even with the prop on centerline, a pitch angle significantly above zero will mean that there is a vertical component to thrust (in a Cessna, far far forward), and removing that will give you a pitch-down moment.
You can use the thrust=altitude, pitch=airspeed to get started, but it's a fairy tale not that much better than telling kids that to go down, you push on the yoke. An adjustment in sink rate at constant airspeed requires
both a throttle and a trim change, and neither is negligible. And some left rudder, too, just for good measure. This is the point of a "stabilized approach."
The OP's question has been answered, but I'll repeat it. The way you get it in your head is to do it. For a while, you're going to have to think about it.
I prefer an options list. If fast and high, pull the throttle and pitch up. The speed is more important than the altitude for energy management (total energy scales with v^2, but only linearly in altitude). If fast and low, just pitch up. If slow and high, pitch down. If low and slow, add a bunch of throttle (you're probably behind the power curve) and pitch down. Repeat as needed. Retrim after every step! If not stabilized at 100 AGL, cram the throttle and go around.