sheppey, you are of course correct in that what approach flight path a light aircraft flies can vary significantly and be perfectly safe, unlike larger transport category aircraft where what constitutes a safe approach path is much more constrained. However the concept is fundamentally the same. If the aircraft is not doing what you want it to be doing at 200 ft than it is usually better to go around then try to force it back to where you want to be in the little time you have between 200 ft and the flare.
Also understand this is for student pilots. A high time pilot can make almost anything work on an approach, a low PPL not so much. However even then high timers sometimes have to throw a bad approach away. Last fall I was going to a small airport to do a flight test in my Grumman AA1 that I had not seen before with a shortish runway. Trees at the end and the way the ground sloped gave the illusion the runway was farther away then it was so when I turned my usual tightish base it left me high and fast on final. Even a full slip was setting me up for a mid field touchdown instead of the planned 300 ft from the numbers. I could have made it work but the approach was unstable because the aircraft was not on a flight path I wanted and fixing it would have involved some excessive maneuvering, so I went around, adjusted the circuit and the next time the approach was setting me up to touchdown exactly where I wanted.
As it happened the next day I was No 3 in a 4 ship formation of Nanchangs. After the break, flaps down at the perch and continuous curving approach with 40 deg of bank ( there was a strong crosswind) with the wings rolling level at 200 ft. The flight path and airspeed was at all times exactly what I wanted and resulted in a perfect line up to the runway with almost no variation in the bank angle. It was IMO a good example of a stable approach from the moment I rolled in off the downwind. The mental stable call at 200 ft was a foregone conclusion.
Bottom line the approach could be a power on approach tracking the glideslope of a power off full flap with side slip or anything in between, but at 200 feet either the aircraft will be on the predetermined flight path and speed or not. If it is significantly away from what you have decided you want to see then I think instructors should teach new pilots that it is time to go around. The easiest way IMO, is to get them to do this is to make a point of using the 200 AGL mark as decision point. Calling stable tells me they are thinking about where the aircraft is relative to where they want it to be.
If you don't like the word "stable" pick another one, but to the word describes exactly what you want to see, there is going to stability in the flight path and airspeed from 200 ft to the flare.