Mixing elevator trim to satisfy trim needs for power off/on is common. As Jester said, traditionally that has required thrust changes with the engine but it can now be done with mixing, which is especially nice when faced with a thrust issue on a plane with a spinner aligned with fuselage.

What you are proposing if I read correctly is to increase angle of attack of the wing at low speeds to gain lift. The problem I see is that instead of a parallel course where more drag is accompanied by more power to maintain equilibrium, the scheme suggested will see drag go up and power go down and the obvious crossing of the threshold into a danger zone.

What your wishing to do... is usually done by flaps, where lift is created at slower speeds but remember that flaps usually require keeping some power on. On planes with flaps, I'll mix a slight throttle increase with flaps along with proper elevator trim to maintain pitch stability.