Josh,
Training airplanes take a lot of abuse, and rightfully so. Abuse to the engine is one of those things. Power off descents in the pattern or to emergency landings are part of training, and should be a very big part of training. Every landing power off, and every approach power off, however is not a good idea, and isn't good for the engine.
If you do a power off approach and landing the landing should be made full stop with a taxi back to allow for the engine temps to normalize (more uniform throughout engine), rather than doing a touch and go with a sudden power-up, or a go-around/balked landing.
Shock cooling is a mythiogical, misunderstood topic. Many argue that it hangs over you, waiting to do you in. Others argue that it doesn't exist. Truth is that thermal damage to engines does exist both high and low. Rapid changes do cause cracking, most notably on the cylinder head between the spark plug holes, and can lead in some engines to seizing, or even problems such as detonation, preignition, etc, when unburned fuel and fuel byproducts remain in the cylinder.
Smooth engine operation is a good key to long engine life, and your long life, too. Always try to treat the engine and the airplane as though your life depends upon it. Because it does.
In training, we do see more wear and tear on the airplanes. We're experiencing things in the training environment that we may not do in the real world of flying on a regular basis, or ever. That's the nature of training. These events prepare us for emegencies, form the basic building blocks of our understanding, and develop habits and wisdom for our future longevity in the industry.
Unfortunately, bad habits can also be taught. Among them I see frequently are the mentality that engine failures magically always occur near a runway. Or that only full flap or no flap landings should be taught, or that pitch controls power and that whole debate, or that ground effect is a "cushion of air beneath the wing." I see great misunderstandings coming out of improper training regarding the use of carburetor heat, looking for traffic, proper use of the radio, engine operation and theory, and a very common use of idle power from abeam the numbers to landing a standard method of approach.
Each instructor teaches differently, and that's quite okay. You'll find that by trying different instructors you may gain a great deal of insight that you may have missed with just one. I often found when I was teaching full time that when I hit an impasse with a student, when the student was on a plateau and not learning or progressing, having the student fly with a different instructor often broke that impasse. Other instructors would do the same with me, and it was often the insight provided by a fresh pespective that made the difference.
Where you need to be careful is absolutes. When you hear people telling you to always make power off approaches or landings, that should throw up a red flag, just as the idea that one should always make partial flap landings in a crosswind should throw up a red flag. You'll find that the folks making these statements are not out to cause harm, but operating within their own safety zone based on limited experience in a particular area...and you'll find that there's usually more to the subject that you can learn. More to benifit you, and choices available in the cockpit than those sets of absolute define.
In the air, there's often more than one way to skin a cat. Power off approaches and landings as a general practice are bad form, in many aircraft. Fly a turbine airplane and that changes...power off doesn't hurt anything, most of the time. But a piston powered airplane, especially a geared piston powered airplane, a power on approach followed by whatever power is necessary to land under given conditions, is more typical. Again, the circumstances and the airplane, and what you're trying to accomplish, dictate what you use, when, and where. Good luck!
