Thrust and Speed.
Which came first the chicken or the egg?
Pitch Power Altitude Speed.
What controls what?
Well - think of these things...
Some military jet fighters can accelerate to a speed in excess of Mach 1 in a vertical climb...
As a flight instructor I teach my primary students the following. (in low power general aviation training aircraft)
Cruise flight - Pitch controls Altitude. You select your cruise speed with power. (small changes in pitch produce a large change in lift and very little change in drag at high speed)
Slow flight - Pitch controls airspeed, power controls altitude. ( a small change in pitch makes a large change in drag and very little change in lift therefore making the speed change)
They learn it that way and can succesfully operate an aircraft usssing that information....
If I am flying with an experienced pilot, and I ask them to do slow flight during recurrent training or transition to a new aircraft, and usually in a higher performance aircraft, I remind them to adjust pitch and power as necesssary to maintain airspeed and altitude. What a cop out!! I do not tell them how to accomplish slow flight unless they are having trouble. It is surprising how many pilots forget how to precisely control airpeed and altitude especially in higher performance aircraft. If they can make it work acceptably, I do not say anything... Many pilots get into the bad habit of using flaps and gear to control their speed and forget how it really works.
In reality.... Airspeed and altitude, power and pitch are all interrelated.
If we assume that airspeed is controled by power, and altitude is controled by pitch, then what happens in slow flight? Try getting up to lift off speed without adding full power on the runway, and try lifting off without increasing angle of attack or pitching up...
In slow flight, if we want to increase speed, we can lower the nose. (Pitch controls airspeed) When we lower the nose and decrease the drag, of the wing and airframe, the speed begins to increase but at the same time the aircraft begins to descend as there was a decreasse in lift due to the angle of attach change. We notice the descent and add power to compensate. (Power controls altitude).
Again in the low flight senario above, if we want to increase speed and we add power, if we have enough available power, the speed will begin to increase. As the speed increases more lift is produced causing a climb. We notice the climb and slightly lower the nose to compenate. (Pitch controls altitude).. The problem is in a small aircraft the available power may not be sufficient to accelerate the aircraft very much so lowering the nose and decreasing the drag has a more immediate effect.
So in conclusion..
I recommend that flight intructors teach their primary students using small low power aircraft how to control airspeed and altitude as I stated at the top of this post... Cruise and slow flight so not operate the same.
I recommend that flight instructors teach and permit their students to discover that airspeed is controlled by power and altitude is controled by pitch at all times when tranitioning to higher power high performance aircraft. That is one of the most important concepts to learn when transitioning form simple training aircraft into a high performance aircraft.
However, if a pilot can control airspeed and altitude succesfully there is no real reason to force them to adopt any particular method nor does their method need to be changed.
My 2 cents worth
Bill