Other than good practice, I don't think I really understand the logic. If anything the engine is less likely to fail at a low power setting during final when compared to any other part of the circuit (carb ice discussions to one side for the moment, that is down to equipment and technique).
Going back a bit in the thread, I know.
So what's wrong with good practice? And can you casually put carb ice discussions to one side?
What I cannot understand about this thread is why anyone would want to carry out a low, powered approach when they don't have to under normal visual conditions, as opposed to a glide final approach from the start of the base leg or from a straight-in approach. Unless the wings fall off a glide approach is going to succeed, assuming you chop the power and set carb heat at the right moment, and you can always get rid of excess height in a slip. A powered low approach carries a risk of engine failure, however small. Why take the risk if you don't have to?
As for big wide circuits with long approaches for ab initio students, I have always thought they are fraudulent. To only get 4 landings in an hour's flying is a total waste of a student's money, and students are well-advised to avoid schools where this happens, which probably means avoiding schools based on busy airports.
PS The reason I was taught to use a 15-sec burst of power with any engine with a carburetor (spelling?) every 500 ft in a PFL or such-like was to get rid of/prevent carb ice, as well as, with a Gipsy Queen only, to clear the plugs and see if the mass of iron was still functioning at all.