There are mixtures of ideas in this thread possibly because there are alternative CDAs. Procedures designed to transition from cruise altitude into the TMA and thence onto the final approach, differ from those used during final approach for NPAs (Constant Angle NPA).
In the first case the initial procedure designs were to reduce workload and increase efficiency / economics; now days they are more biased towards flow management and environment / noise. Whilst the most efficient descent may be a glide, such a procedure cannot accommodate different aircraft types and give ATC full control of speed. Thus descents into the TMA are compromises, but even for a standard profile the variability of wind, power requirements (configuration / icing), wt, etc, results in a range of operating techniques from power-on to flight idle + airbrake. An FMS (VNAV) based procedure gives the crew the big picture and a ‘how goes it’, whether flying on autos or manually. Non VNAV aircraft require information of track distance to touchdown so the crew may calculate the profile and also judge a high or low energy state.
A CDA on final approach has been promoted to reduce CFIT on NPAs; this avoids step downs during the procedure, and normally mandates a GA at MDA if nothing seen. A difficulty for the industry is to train crews to adapt from a decelerating approach on an ILS (where the vertical path is constrained), to an open vertical path (unconstrained) on NPAs. Recent CFIT accidents and incidents recorded crews flying VOR/HDG and VS during a decelerating NPA; they forgot the basic flight mechanics that a deceleration at constant VS will increase the flight path angle and aim the aircraft short of the runway; thus during a CDA on a NPA, the VS must be reduced as speed is reduced. To combat these problems some operators now fly constant speed / configuration NPAs. Flight crews should carefully brief NPAs, use the tables of range vs distance now on the charts, and treat all NPAs as something very different and potentially hazardous.
In non VNAV aircraft I preferred to fly manually, this gave a better feel for the aircraft both in control force, trim (speed), and deceleration (energy management). Of course if the workload increased and/or the monitoring pilot was tasked elsewhere then I used the autos, but preferably in HDG with speed on pitch, the rate of descent being controlled with power / airbrake.
Thrust provides energy, the elevator distributes it.