I'm one of those who do believe "shock cooling" is possible because I've changed out a lot of cylinders that have been cracked as a result. I've seen it happen.
You're talking about different things. Thermal issues are entirely different than issues related to backlash in a gearbox.
Smooth power management has more to do with detonation issues (pushing too high during a power transient on a boosted engine with a leaned mixture, typically) and engine longevity and balance (such as detuning a crankshaft), or merely keeping the engine operating (I had an engine failure in a J-3 cub when I applied power to go around for some deer on the runway, many moons ago...I pushed the power up too fast, and then I didn't have any power at all).
Graduated power reductions such as the inch per minute/inch per thousand feet rule of thumb are more grounded in tradition, but they're a nice, conservative way to operate the engine, be nice to the turbo and turbo bearings, and add to the long life of the engine.
When I was flying radial engines, we made a lot of big power changes; we'd reach the edge of a mountain and push over the top, following it's contours down, slipping the airplane like a cub (big four engine airplane), and use the power accordingly. The airplanes and the engines took a certain amount of abuse, though we tried hard to be as nice to them as we could (treat it like your life depends on it, because it does). No opportunity to wait a minute to reduce an inch of manifold pressure. What we did do was limit the lower end of our power reduction. We ensured that we had adequate power available to keep from driving the prop with slipstream. This in turn meant limited ability to control airspeed on a steep downhill run, which lead to slipping, use of flaps, and judicious use of terrain and planning where to roll into the run and minimize the airspeed buildup. In other words, we had to fly the airplane.
This is really what these rules of thumb are about; treat the airplane as well as you possibly can. You have a lot riding on it. You.
Places where this really shows up go beyond merely enroute climbs and descents. I see pilots who shut down their turbo'd and normally aspirated engines as soon as they reach the parking spot. We warm an engine up after it's started (we should), and we need to cool it down by running it after we stop. This is especially important of a turbo'd engine. In either case, the engine should be leaned back and cleaned up prior to shut down and most engine manufacturers recommend final checks prior to shutdown...things your flight instructor almost certainly never taught you, and that aren't in your aircraft flight manual...but are in the engine manuals from the manufacturer (which your instructor probably never showed you, or as seen him/herself).
Some of your biggest thermal changes take place in that engine upon shutdown, when oil stops flowing to carry away the heat, when it's no longer circulating but sitting on bearings where it can boil and coke, and where airflow no longer exists to put fresh, cooler air over cylinders and the engine in general. Preparation for that phase should include a cool down period, which is every bit as critical as a warm-up period after the engine is started. (Bear in mind that on exceptionally warm days, engines can overheat during ground operations, and excessive ground run time can do more harm than good). This is a good time to check idle mixture, too.
Closing the throttle in the flare isn't the same as a power off approach and landing. It's just part of a landing technique. Vary the technique as you need to at the time, considering the conditions that exist at the moment you land.
Although it might take some amount of power to maintain airspeed & a proper glidepath in a given configuration to your aimpoint, the wheels should touch the runway with the throttles idle, I don't care what airplane you fly.
You should care, because it can and does make a difference. With more experience,you'll learn this. Power may be carried for wind conditions, such as assymetrical thrust to compensate for a crosswind. It may be carried under particular soft field conditions (not the cheesy kind that everyone thinks they're doing in training. Real, genuine soft field conditions). Touching down with power is often prudent on skis, in snow, on mud, and other such scenarios. I've found it very prudent when settling onto a frozen muddy runway, as weight as slowly applied to ensure the aircraft won't break through. In turbine airplanes, it's often not only prudent but necessary, to have the engines partially spooled, and to carry the airplane until touchdown. Power may not be removed, in some cases until the airplane is firmly on the wheels. Some fields, the shortest ones in the world, require that the engine be spooled and coming to full power by the time you touch down...carrier landings.
Don't speak in absolutes so much, as you'll find as you gain experience that your absolutes of today don't mean much tomorrow. The more you learn, you'll learn that the less you know.
Radials, schmadials, this isn't about engines that have to be catered to. This is about trainer airplanes with small 100 hp engines that do power off glides and landings all day long. Most every one says power off landings are good training and everyone agrees.
Enough with the 'big engine' talk that scares the beginner student pilot in his C-152.
A student pilot asked about radial engines, and was given the courtesy of a reply.
The same principles apply to an 0-235.