So if the 'hybrid' takeoff above really does have all of these
advantages, why isn't it 'recommended' per the FAA handbook?

How do you guys do it?

I've found that on a hard surface runway (in a Cherokee), between the
time I start rotation to the time the wheels lift off, I've already got
flying speed. I've done the "lower the nose to accelerate in ground
effect" thing but I don't get more than a few seconds of that before I'm
already past climb speed. On a short field, every second matters, but I
expected more of a difference.

The Cutlass (C-172 RG) POH says, for high altitude, to lean to best RPM,
and (if I remember right) use a notch or two of flap. But the odd thing
is that the POH says to hold the wheel back during the takeoff roll,
rather than let the airplane accelerate on the ground first. The
airplane will start to take off and gently bounce on the runway a few
times as it builds speed.

Seems to me this is wasting energy somewhere.

Jose
--
"Never trust anything that can think for itself, if you can't see where
it keeps its brain." (chapter 10 of book 3 - Harry Potter).
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