What's the purpose of partial autopilot disengagement after applying certain force to the control wheel?
The autopilot will disconnect on large control inputs because this is the most intuitive way to control the plane. On Boeing planes, the controls will physically move along with the autopilot. If the plane starts doing something you don't want it to do, the instinctive action is to grab the controls to correct it. While the autopilot button would normally be the way to disconnect the autopilot, it may not be the instinctive way in an emergency, and it can be helpful to already have both hands on the controls when the autopilot disconnects, rather than having one hand disconnecting the autopilot.

The reason for only disconnecting one part of the autopilot could be to help the pilot. Maybe there is a problem with the elevator controls, or an upset that affects the aircraft primarily in pitch. Maybe the TCAS gives a "climb" command. The pilot wants to take over pitch control to address this situation, but other controls are fine. While the pilot now has control of just pitch, the autopilot is still taking care of the other controls. The autopilot only gives the pilot control of the modes that are being overridden, instead of just turning off and requiring the pilot to deal with all control modes.