I am aware of a number of real engine failures that occurred on application of the throttle after a simulated engine failure.
Clinton,
As I am, and in each case the failure of the engine to accelerate was put down to icing, the "carb" heat was not used during the descent at idle, and the engine wasn't "cleared" during the exercise. One particular PA-28 carb. engine( depending on the venturis fitted) is particularly prone to ice buildup, as are many smaller Continentals.
No piston engine is immune, regardless of carb. or injection.
Another "potential" problem with just "pushing the mixture up", if the throttle has not been closed after the mixture is "pulled" ---- all too easy to do if there is need the power in a hurry ---- can result in an engine overspeed, with all sorts of potential damage, starting with the crankshaft counterweights, if your engine has them.
As I keep on saying, don't shut the engine down at all, and keep it a bit above idle, with anti -ice heat as required.
In practice current manufacturers manuals are an interesting animal ---- I have "old" and current editions of engine manufacturers manuals, such as the Lycoming IO-540 in Comanche 260C, they are quite different. The mid-1960 or so manual had all the details for running lean of peak, not so the more "current" manual I have.
Tootle pip!!