I agree that some types have a best glide speed, and a Vx very close to each other, and that sounds happily safe. (Like having Vmca ans stall speed very close in a twin). I also know that pilots with practiced skill, be it unusual skill or not, can be really good at a precise flare from a "slower" power off speed - excellent! I know that ground effect can be favourable factor on a landing, but is not a dependable a way of preventing a hard landing. I also know that When you flare, particularly from a steep approach, (like power off), you're expending energy you've stored in airplane forward speed, to accelerate upward away from your descent path, enough to [hopefully] have your path be parallel to the surface. That acceleration means a very slight increase in G (acceleration), so the stall speed will have a very slight increase. So, stall speed is slightly increasing, while you're pulling to precisely time a flare, having that little bit of extra speed is nice then.
I also know that I have flown the certification flight testing for STC approval on several modified types (C150, C182, C185, and C208B) for 23.51, for this characteristic. I have found myself surprised that the slower power off speed required very much more application of skill to result in a suitable EFATO landing, and that was when I was expecting it. The opinion I hold is based upon my experience doing the testing. As a result of my testing, and the data gather, an STC was issued. In one case, the procedure to climb away slower than Vy had to be a special condition on the approval for lack of compliance (everyone agreed that compliance could not be shown for an EFATO at Vx).
My self designed exercise in power off descent and arrest at altitude was devised to remove the need to do this close to the surface, while still being able to demonstrate the effect. It has noting whatever to do with "landing" the plane, but rather managing the energy of the airplane, to save some for when you're going to need it at the flare. The lesson is your personal level of comfort in having, and being able to apply the reserve energy to momentarily arrest the descent at an altitude, as though you were landing there. When I train this, well briefed, nearly everyone I do this with falls through the hard deck with the stall warning blaring - which as not a nice way to be approaching the surface.
Unlike airplanes, helicopters have (by certification requirement) a height/velocity "avoid" curve presented in the flight manual. Because it is understood that from certain combinations of low altitude, and slow flight, a safe power off landing cannot be considered safe for the average pilot. I have also been trained to do autorotations from within that "avoid" range, it's very skill dependent. The same physics applies to airplanes as helicopters in this respect, though with different numbers. And, helicopters have an advantage that airplanes do not have for power off landings, as they can store energy both as forward airspeed, and as excess rotor RPM, where the plane can only store it as airspeed when that's spent, you're done.
What any pilot does, is up to them. I just would like pilots to consider a lesser known and understood factor which affects the safety of power off landings. I do not needlessly climb away at less than Vy. The three EFATO's I have had have all resulted in a no damage landing ahead. The flight testing I did for this nearly resulted in a damaged plane - when I was completely practiced and ready for it!