On airplanes without flight envelope protection, the pilot needs to feel how much force they are applying to the flight control so they get a feel for how close to the edge they are getting. That is the reason for the regulation that requires the control force to increase linearly for each additional increase in pitch attitude — and the need for MCAS, which restored that linearity at very high pitch angles on the MAX (by de-trimming the elevator).
Accordingly, in manual flight, there is no auto trim. The pilot puts the airplane into the desired pitch attitude using the elevator, which deflects enough to provide ample pitch authority, and then must manually trim out the yoke force using the trim switch or trim wheel.
The autopilot auto trims soon after changing pitch with the elevator. This minimizes the chance that there will be a residual yoke force which the pilot does not (cannot) anticipate when the A/P is disconnected. Such residual force, suddenly released when relinquishing control to the pilot, is essentially an abrupt control input, which at best can be upsetting to passengers, at worst can cause injury, structural damage or loss of control. That is also why the A/P will not engage if it detects force is being manually applied on any of the controls. It is also why the first step in the stab runaway procedure is: Control wheel — grasp firmly; before turning off the A/P, as it likely had already begun using the elevator to counter the runaway.
If the stab were to work as suggested, holding the yoke at its stops would effectively start a stab trim runaway!