DB - yes, from my experiences I'd agree something is missing from training here. And as you say SAS, some training in the actual aircraft is essential.
Basically I set up what I thought was going to be a simple verification exercise of my matter of fact comments on recovery from UA from poor use of GA. Straight and level at 2000ft, reduce Tq to low level, watch AS decay to 80 kts or so, select GA and wait. After a minute or two, after the initial climb, AS had decayed to 30kts and reducing, VS to 300ft/min descent and increasing, attitude 10 deg or so nose up.
From a pretty uncomfortable attitude, time to intervene by hand. Simple - wings level, forward cyclic to obtain I thought say 5 deg nose down, watch AS, as exceeded 40 kts ish pull power, level pitch, sorted. Except it wasn't quite like that.
The big thing that surprised me - and alarmed me - was how slow the acft was to react to forward cyclic forward and reduce the pitch up. Despite what I thought was an appropriate forward movement, nothing happened for several seconds - the cyclic seemed initially completely ineffective. Eventually it lazily did what I wanted. Then I found that although pressing trim release, I'd forgotten to uncouple GA, which was still on and resumed as soon as I released trim release after recovery. So I did it all a second time, first uncoupling GA, then trim release. Same initial cyclic laziness but at least no risk of the upset happening again from re-engagement of GA. But - two buttons to have to remember to press in a crisis!
Don't get me wrong, this wasn't a major drama, just a bit disconcerting and certainly illuminating. I'm not sure if this little exercise was truly representative of how things really feel with other acft in a similar situation - quite possibly. But I'd never experienced this in training, and it would have been good to have done so and learn to patient and be confident recovery would follow. As we have seen from the Cougar incident and possibly the Sumburgh accident, autopilot mis-handling can lead to exactly the type of phase of flight I experienced.
With regard to training/learning tools, it did occur to me that it would be good if the controls were data logged so movement extents and rates etc could be reviewed in a de-brief - and initial briefing. Does this happen on heavy acft training?
And DB, your point on caution on experimentation is well made and indeed occurred to me too!