|I see nothing wrong with practicing power off approaches in training (or other times if you'd like) - any airplane can do a power off approach; gliders do it every time and so does the space shuttle, both with drastically different glide ratios!
This thread essentially started because of a remark I made in another thread that I hoped students weren't being taught to do power off approaches. I meant to say that they shouldn't be told that all their approaches during training and while flying cross countries and such should be down power off. There are a number of good reasons why, in the main, you should be flying a powered approach. Why do commercial airplanes always fly powered approaches? What happens to the descent angle when flying a power off approach in a powered aircraft?
I think it's pretty obviously why airplanes need to fly a powered approach while on an instrument approach so this mostly deals with visual approaches. It is generally easier to fly a stabilized approach while under power. In both cases, powered and non-powered, you can trim the aircraft for a certain speed and the airplane will do a nice stabilized descent. The problem is when you need to adjust that profile either because of a miscalculation on the pilots part when setting up the approach path or due to a change in wind. When the power is at idle, your only option is to add power - that becomes a problem when you have performance enhancing wind shear. You could argue that to fix the problem you could sideslip but that requires more effort than adjusting the power, and puts you and all your passengers at an awkward and uncomfortable angle. On a windy day, flying in and out of sideslips can be quite a bit of work and not that pleasant. While flying a powered approach you don't have that problem (as much) as you are able to reduce power to counter the wind shear. Or the case where you end up not being able to make the field and you need to add power - now you're doing a powered approach, unless you want to keep power on until you're too high and then cut it again...
How do gliders do it? Spoilers and speed brakes which are easy to actuate and control, and can adjust the flight path with precision. Generally, a well flown approach in a glider will have spoilers partially deployed for the majority/all of the approach. It's actually quite similar to the throttle in a powered airplane.
What about flaring? If you have a private license you should know that coming in either too shallow or too steep makes it more difficult to flare properly. There is a nice sweet spot for most aircraft that's right around the 3 degree slope, plus or minus a bit. Flying a power off approach at the proper speed requires you to do an abrupt flare at a very precise distance above the runway - slightly too high and you'll smack it on, slightly too low and you'll smack it on; quite hard usually in both cases. A way around this is to carry higher speed during the approach so that you have enough energy to pre-flare, shallowing out the approach path, so that you can make a normal flare. This is nice and fun to practice but requires more skill and attentiveness to land smoothly and precisely - it is easier to mess this approach up than a powered approach on a 3 degree slope.
Another problem with power-off approaches is engine spool up time in the event of a go-around. That's a big reason why jets don't fly power off approaches, even with the improved spool up times of modern turbofans. In pistons, if you're too aggressive with adding power you can get the engine to cough and sputter and depending on the conditions and the engine, it might quit. Adding power properly (smoothly) solves the problem and this usually isn't a big factor on piston airplanes.
If you are to change the trajectory (direction component of velocity) of an object, you must accelerate that object. Force causes acceleration and they're all related to inertia and energy. Essentially, it takes more energy (and time) to change the trajectory a greater number of degrees - should seem obvious. When flying a power-off approach you will generally be at a significantly higher angle than 3 degrees (unless you're a glider). If you're required to do a go-around, you will require more energy, time, distance, and altitude to be able to get to any point on the go-around compared to an airplane flying a powered approach around 3 degrees. I could do the calculations to see how much more energy is required (since your engine only has a limited amount of power, that extra energy comes from time, which means extra altitude and distance being used) but I think that'd be a bit much. Just consider that this is not a linear increase in energy required, it's an exponential increase - Kinetic energy = 0.5*m*v^2 - a change in 'v' requires an exponential change in kinetic energy. This boils down to being a safety factor. At most approach speeds you'll need to add power as the first action of the go-around - this accelerates you towards the danger that you're trying to avoid by doing a go-around. That's 'undesirable' but if you were to give in to your fear you might pull up first before adding power and depending on a number of factors, you might stall - in any case, you've increased the probability of stalling. By flying a 3 degree powered approach you have more margin for error in a go-around and you're less likely to screw it up.
Another reason to avoid flying power-off approaches is shock cooling. Need I say more?
Flying power-off approaches is a nice way to 'switch it up' and/or improve your flying skills but there is a time and a place for it, and I don't believe it should be taught as the approach to be flown under "normal" operations.