Now if you did a check on one of my old students you wouldn't have a clue which method they were using because just because they have gone solo doesn't mean the approach teaching has stopped there
I cannot believe that you would teach a technique and then not even have the decency to tell the student what they are actually using. Not only is this important for their knowledge but it might be handy if they ever do some training elsewhere.
Its a bit like giving somebody a fly fishing rod and telling them to throw the hook at the water. You might not realise but there is a lot more to it.
I cannot imagine EVER hiding information that is that important from my students. You mention that the learning process doesn't end just because they have gone solo. My point is that not telling them how they are flying will prevent them from going solo sooner. And lets face it, surely it would be nice to know that "Pitch for speed" is the name of the method, why because it IS the method. And likewise for "Point and Power"
After all isn't it more important that we get people to a safer standard sooner?
And as for the pitot failure circuits I'm sorry I think I am failing to understand your point here. For a PnP student they will be able to keep the same aiming point and the same RPM and the picture will stay the same and they'll trim.
And then in a nil wind day they will fly with a constant airspeed all the way down to flair point and then they will flair. On a windy day they will probably come in with more power and faster which will keep them safer anyway.
Surely that is easier than the Pitch for Speed guesswork?