Hi Capt PB
Yes, I know both thrust and pitch have effect in both path and speed, but:
Isn't it easier to "divide" the tasks in our brain (or in the FCC or FGC or whatever) and assign flight path to the pitch input and speed to the thrust input?
It is like dutch roll. Automatic dampers use yaw. But damping it manually is better done with roll, they say. They are interrelated motions. Each variable affects the others. So all variables should be considered. Letting one constant helps.
Of course, if you want to recover the G/S from slightly above with correct speed, you know that you will need to reduce thrust in addition to the lower pitch command, so you do it before the speed increases.
I guess it is all about energy state, instrument scan, attitude and thrust changes coordination and experience (a "model" in computers). Computers have a "super" scan rate, and trend sensing, and gains, and many other things I have never heard about. I think that the path-pitch and speed-thrust "alocation" is good for both computers and humans.
In an ILS, I know that many use thrust for glidepath and pitch for speed. But in level flight, I think we all do it the other way round. Because it is easier, or more intuitive, if you like.