So many techniques filter down to GA from Airlines and are assumed to be better simply because that's the way the big boys do it.
Yes indeed.
Would those advocating the stick for speed method push the stick forward if low and slow? Of course not, so why confuse a student with that technique?
Well, I certainly would, if the airspeed was dangerously slow. I would have thought that this response would be instinctive for all properly trained pilots(?) Better to risk landing short - but under control - then to risk a stall at low altitude. Hauling back on the stick to 'stretch the glide' has killed lots of pilots over the years (see further Langewiesche, especially Chapter 14).
If "low and slow", one is faced with two distinct problems; IMHO, the proper course is to lower the nose
and add power (or close the divebrakes, if flying a sailplane).
See generally
"Where Does Airspeed Come From?"