How were you taught to climb and descend in your primary trainer (Cessna/Piper)?
To climb: Apply full power and select the pitch attitude to achieve 70kts. Then maintain the speed with small elevator inputs.
To descend: Close the throttle and select the pitch attitude to achieve 70 kts. Then maintain the speed with small elevator inputs.
In both cases, the power is ‘fixed’, inasmuch that the throttle is either wide open or fully closed. The elevators are controlling the speed (which of course doesn’t have to be 70kts; that was just an example).
FLCH is the same in that the thrust levers go to “full power” for a climb, and “idle” for a descent*. The elevators control the speed.
The FMAs show that FLCH, VNAV SPD and TO/GA are the only ones where the auto-throttle is in a “THRUST” mode and the elevators are in “SPD” mode.
All other modes have a “defined vertical trajectory” which is controlled by the elevators; the auto-throttle must therefore control the speed.
This applies to ALT HOLD, V/S, G/S, GP and VNAV PTH.
*I agree with Wiggy that later models have an intelligent FLCH and TO/GA, which don’t use just full power and idle, but to try and explain the principle to someone unfamiliar with AP and AT modes, the “binary model” may help understanding. I would also leave out VNAV to start with!