During last fall's flight test program with a highly modified (and draggy) Cessna Caravan, it became necessary to reduce the published Vy, to obtain the minimum required climb rate to pass certification. Because of the added drag, Vy reduced a little = less drag, so better rate of climb.
Once I declared this, Transport Canada said fine, but that means that your target speed at 50 feet will now be the lesser speed to be declared Vy, and therefore I was required to demonstrate an EFATO from 50 feet, at that lower speed. This was not required for the lower yet Vx (thank goodness!).
At my new Vy, this was only just achievable, and was indeed to most scary thing I did during all of the test flying for that program. I had to admit that a few times, it was necessary to add power on the way down to make it work (and adding "a bit" of power in a Caravan is not as easy as it sounds).
The manuever was akin to autorotations, in that prompt and considerable "down" control was required, with the intent to accelerate, and then an agressive flare at the bottom. This required considerable practice, and was very stressful in a new plane, which was supposed to be landed nose low to prevent a groundstike of the payload.
We all agreed that the maneuver could be done, on the premise that the aircraft did not have be undamaged after landing, just no one hurt. That would have been doable.
The popularity of STOL kits also brings this to the forefront. Whether it is an EFATO, or simply an approach flown rather slowly, the very real hazard is there. In the early days I remember finding that my STOL C150 would very happily glide at 50 MPH, rather than 60+ stated in the flight manual. This was fine "up there" but very risky close to the ground. You could approach the ground power off at 50 MPH, but you had no inertia left with which to flare. Just slamming into the ground unarrested was a very real risk. Again, akin to the autorotation, where if you have not built up rotor RPM for the flare, you're just going to hit the ground.
Though flight training should teach the basics of this, the "fine points" are sometimes not understood by the instructor, and not taught well. In general, many aircraft will fly certain maneuvers at speeds less than the flight manual stated speed, but if the engine quits, you will no longer have the margin to maintain safe flight for the FAA's pilot who is flying without applying "unusual skill, attention and strength".
Though never to be published, for my Caravan program, I was required to fly a Vref -5 circuit. From liftoff to touchdown at my new speeds -5 knots. I did it, but the stall warning was sounding through most of it. That was the required margin between "normal skill and attention" and what I should be able to demeonstrate with my total of 40 flight test hours on type!