I’m very skeptical of that, very.
I would wager that most all of us fly the initial climb in a trimmed configuration at or near Vy. If it was that easy to prevent a departure stall, the accident statistics would look a bit more rosier. I suggest you go out with an instructor and have them do some simulated power loss on departure scenarios at altitude and just watch how fast the airspeed and energy decays - it’s an eye opener.
I don't think it's as simple as being purported. What works for some airplanes may not work for others.
The trim detail is correct, an airplane, in steady state, will maintain its trimmed airspeed. In other words, an airplane that is not accelerating (+/-) will maintain it's trimmed airspeed. If you reduce power the nose will drop to maintain its airspeed. If you increase power, the nose will rise to maintain trimmed airspeed (and you climb). Of course nothing is perfect, but it is generally true.
The issue I see is with high powered, heavier airplanes. In the 22, you apply full power, accelerate to 73 to 77 knots depending on model, lift off, the airplane continues to accelerate, in other words, the trim state is constantly changing. You take off with 50% flaps, the airplane accelerates to 90 knots, at that airspeed and clear of obstacles, you go to 0 flaps, another trim state change. You accelerate to Vy (98 knots), more trim change, you stay there until you are comfortable with your altitude, then accelerate to 115 or so knots, another trim state.
I just trim away excessive pressure during this phase, how much changes depending on fuel load or passenger load.
So being trimmed correctly and "allowing" the plane to save itself may work for some airplanes, but I'm thinking it probably won't work for most. Being low, with a dead engine, is not a good time to find out. Better to be proactive imo and make sure the nose goes down and the plane reaches best glide.