The starting point for more commonly encountered emergencies would seem to be rehearsed reaction. For example, the newly minted PPL who suffers and EFATO will gain very little from an assessment of the situation that takes him outside of his training. Deciding to turn back to the runway at 700 feet because he thinks there are good reasons to do so is far more likely to land him in a whole heap of trouble (pun excused).
However, every student and every pilot is different.
The PPL syllabus has to cope with the eager and quick to learn 22 year old and 50 year old dog trying to learn a new trick or two.
There is ample opportunity with the former to look at different emergencies and to explore the ways with which these might be dealt than with the old dog where it is as well to feed them with the rote solutions to common emergencies.
Many of the rote responses to a given emergency exist because experience tells us that they work (in the vast majority of cases).
Chucks example I think illustrates the point. Perceived wisdom would probably have been to take the problem into the air as others have said. On this occasion that was the wrong decision. The time taken to consider the options was valuable, but perhaps the value only came with considerable experience. In other words would a less experienced pilot on average have been better going with the perceived wisdom.
The ability to deal with an emergency "comfortably" and well comes with experience. With time and by flying regularly you start from an awareness that your basic handling skills are sound. Moreover you are comfortable handling the aircraft in most configurations and have a pretty good idea of how it will perform.
There is no doubt gathering that experience can be hastened by taking every opportunity to fly with others who are able to confront you with different situations and allow you to explore the handling limits of the aircraft. Instructors should take every opportunity to do so at the renewals and pilots should take every opportunity to fly with instructors and more experienced pilots.
Post PPL there are a number of things you can do. An aerobatics course is a good idea. It will improve your handling skills, your reactions and your knowledge of the envelope of the aircraft immeasurably.
I think flying more complex types is another excellent idea. Having done a MEP course when you fly usually much slower and less complex SEPs you will find that you are so much further ahead of the aircraft.
Personally, I am not convinced that flying a great number of different types achieves a great deal. On the whole a tailwheel is just like a tricycle - except on the ground, a balloon is so totally different that the skill sets will rarely converge etc.