Scudrunners

I agree, Paul, with the extra energy potential of using the entire runway. You reference altitude as that extra energy, potential energy of altitude. Consider the extra kinetic energy, zoom reserve, of staying in ground effect until cruise airspeed. Either can be applied to the engine failure problem.
I have had thirteen engine failures, all but one at very low altitude. Most happened in pull up from a crop field or in the crop duster return to target. The one on takeoff was just after getting into low ground effect and I landed on the remaining runway. I would have been less comfortable at a higher altitude.
The kinetic energy crop dusters develop on a spray run is entirely sufficient to zoom up to higher altitude followed by an energy management turn to a near safe landing zone. We turn very steeply, but at little more than 1g. Simply allowing the nose to go down naturally in the turn creates no load factor.
I really believe we instructors contribute to takeoff and go around stalls by overestimating the value of altitude. Low altitude orientation preaches that kinetic zoom reserve in airspeed is more important than potential energy of altitude until high enough to safely recover from an inadvertent stall. When high enough to recover, kinetic energy (airspeed) is not more important than altitude. On takeoff or go around, airspeed is more important than gaining altitude quickly. Level in low ground effect is a good place to sort things out.

Different aircraft can store different amounts of kinetic energy depending upon their drag.

Anything over 185 mph is wasted in a Pitts S-2B, I know from experience. You hit a drag
wall at that speed.

Contrast that with say the -104. I know that Dear Old Dad is considered a really shitty stick
by the TC Experts in Canada, but at Mach 1.3 at the surface at Primrose Lake, if the throttle
went back to idle, he could zoom up to 30,000 feet and do a simulated forced approach to
Cold Lake and land without touching the throttle, because the -104 stored kinetic energy
really well, and he was a really shitty stick compared to a Tower C Big Belly.

Also something to consider is the aspect ratio of the wing, and it's effect on drag as the G
goes up. The P-51 for example had a nasty, fast thin wing that bled energy horribly over +3G.
I know that because I'm such a shitty stick compared to say an obese TC Inspector that can't
land a Cessna 140 and tells everyone that I run coke up from South America.

Rob Holland - another really shitty stick by Canadian standards - told me that if he accelerates
in ground effect, he gets another 10 knots in the MX2 by the end of the runway, which is nice
for the pull/push to the vertical, which all Canadian pilots do at the end of the runway, right?