You make it sound like students are doing roller coaster rides down the final approach. Which I will admit does happen in some cases with both techniques.
And again one method clicks with one student and the other with another.
There is no safety issue with either method. And some students find easier/progress faster using one method than the other. Which one the instructor starts with doesn't really matter its just a means to an end to get the pilot linking there control inputs. As you quite righly say start anticipating what the aircraft is going to do for a certain enviromental effect and approprate control input.
Lets start getting the whole of the UK teaching stalling correctly then start worrying about two perfectly safe methods about flying an approach.