Like the situation OP says: you scan instruments to analyze the situation, determine what to do to recover and apply that procedure. If it doesn't work, or something else goes wrong during that procedure, you adapt to another procedure. Remember, that during every flight with an instructor, you're being trained on one thing or another, so after a while all the "emergencies" seem routine. You'll be turning onto Final to land and suddenly your instructor will decide that your flaps failed so you have to land without them, or just as you're flaring for a landing he'll tell you to go around, etc.

It certainly results in well-trained pilots, but it also gets very boring.

The immediate reason to stop was the fact that the more I did it, the more nauseous I got, but by then I had already decided that flying was not nearly as exciting as I expected it to be. Stopping was an easy decision to make.

That said, I also have friends who still totally love it.