Having said that why does the Citation I fly use pitch for descent on the glideslope autopilot engaged and thrust to control speed? Obviously that works too.
That's a very different situation because the aircraft is artifically constrained into a lateral+vertical flight path.
When you are flying a coupled ILS, the autopilot pitch and roll servos are driving the ailerons and the elevator to maintain the localiser+glideslope. The pitch trim servo is concurrently trimming out the elevator trim tab so as to minimise the pitch servo torque. And the yaw damper is also doing its own thing with the rudder...
The autopilot doesn't care what speed you are doing. It will drive the control surfaces purely to maintain the LOC+GS. You don't have an autothrottle...
This brings many gotchas e.g. it is easy to end up on the back of the curve and then you may not have enough power to recover while maintaining the glideslope. Turkish 737 in Amsterdam... Thompson did it with a 757 at Bournemouth but they got away with it.
You get funny things happening when on autopilot e.g. you are flying along and suddenly your airspeed has shot up. But your altitude is constant (obviously). This is because you are in an updraught, so the AP pitches down to maintain altitude, so the airspeed goes up as a consequence. Or the reverse, in a downdraught.
But I am sure you know all this. The autopilot scenario is a total redherring.