Isn't it so that the elevator trim simply runs to unload the pitch actuator? The autopilot "tells" the actuator to exert some force and then the trim runs to zero the force, so that it's not a highly intelligent system.
Once you drop to an arbitrary bug speed do you really want to depart the glideslope in the direction of terra firma to depend on the GPWS or EGPWS? If you bugged a too-high speed that could have really unwanted consequences so that I think it might be better to stick with what we have, the autopilot chasing that sometimes elusive glideslope and the autothrottle or the Pilot Flying sorting out the more-stable speed. You can fly off the glideslope a lot quicker than you can change the speed, in other words. Too, once you have the glideslope at full scale, when that won't take very long, especially close-in, that mandates a go-around. The same sort of incapability that might let speed drop might also lead to an attempt to recover the glideslope despite what the rules say.