Can I ask if you actually fly planes? Moving the trim is exactly how most autopilots work. I usually fly the 172 and pitch changes made via the autopilot (I am usually flying with a GFC700) are done 100% via actuation of the trim wheel -- and the trim wheel is also the main control for adjusting control forces to maintain a given pitch attitude.
Edit: Reading your comment more closely, I think your concern is more to do with the fact that the trim is actuating the whole horizontal stabilizer rather than just the elevator? There is no separate elevator trim on the 737.
Edit: Reading your comment more closely, I think your concern is more to do with the fact that the trim is actuating the whole horizontal stabilizer rather than just the elevator? There is no separate elevator trim on the 737.