Every year a couple of pilots die because they are too slow on approach.
Where I fly, a student will fail his checkride big time if he's only one
knot below the yellow triangle on final.

Assuming the U.S., not likely. I admit that being slow on final is bad
news, but the Practical Test Standard for the private pilot exam calls
for +10/-5 knots as being acceptable for a final approach speed (page
1-16 - see below). If one of my students was "pink slipped" for being
one knot slow on final, I would advise him to challenge the failure -
and he would win. An examiner simply does not have that kind of
latitude. If the applicant flies to the PTS, he gets his license. I
agree that if there is a headwind, "recommended approach airspeed" will
be higher than the "yellow trangle".

Tony V.

LANDINGS
Q. TASK: NORMAL AND CROSSWIND LANDING
NOTE: If a crosswind condition does not exist, the applicant’s
knowledge of crosswind elements shall be evaluated through oral
testing.
REFERENCES: Soaring Flight Manual, Glider Flight Manual.
Objective. To determine that the applicant:
1. Exhibits knowledge of the elements related to normal and
crosswind approach and landing procedures.
2. Adjusts flaps, spoilers, or dive brakes, as appropriate.
3. Maintains recommended approach airspeed, +10/-5 knots.