Well, no. Manoeuvring in the late stages of a forced approach to the runway from circuit altitude and manoeuvring for a forced approach to the runway from 500 agl are both carried at low altitude. Neither is done at 3000 feet.
This at least doesn't need to be a matter of opinion, and is something everyone can try it very easily for themselves....
Sure it will...... eventually. By the time it does, vital airspeed will be lost while it continues to climb. Potential energy, it has to come from somewhere and it sure ain’t the engine.
Trim for a Vy or Vx climb at full power. Close the throttle. You will continue to climb for about half a second, as the nose comes rapidly down and you overspeed. You will need to ease back on the yoke almost immediately to prevent significant and excessive loss of altitude.
If anyone doubts this, it is merely necessary to compare the takeoff trim position, typically near the centre of the trim range, and which is (unsurprisingly) close to trim for a full power climb, to the trim position for an optimal glide, which is almost all the way aft.
if you do intend to maintain a 45° bank turn, the yoke will need even more back-pressure to avoid an overspeed and rapid sink.
It really depends on circumstances. There are lots of airports and runways where landing straight ahead is great advice, and there are lots of places where attempting landing ahead means certain death - for you, your passengers, and possibly for people on the ground who didn't sign up for the risk.Land straight ahead... ...and live.
It's not complex, and need not be risky.This is far too complex and risky to be taught.