Actually, that IS the way they work.
Battery positive voltage is applied from the headlamp (HDLP) circuit breaker in the instrument panel fuse block to both the coil and switch side of the ALC HDLP relay 44. When the BCM receives this signal it will apply a ground to the coil side of the ALC HDLP relay 44. This energizes the relay, closing the switch, and applies battery positive voltage to the headlamp switch and to the headlamp opening door actuator control module. This actuator allows battery positive voltage from the HDLP MOT LH fuse and HDLP MOT RH fuse in the underhood electrical center to be applied to the headlamp opening door assemblies. The ground circuit is applied from G102.
When the buckets raise and reach the stop point, a signal is immediately sent to kill the power. It does not keep trying to raise the buckets for a period of time as you suggest, unless it never receives the kill power signal. Thus, a broken gear will cause power to continually be applied until the preset "time out" occurs, at which time power is then killed.
There is a good deal of torque put on those nylon gears as you have stated, which is why the brass gears are better for that reason. However, I have heard that the gears are nylon for a reason. They are sometime referred to as "suicide gears" because they are the first to go if some type of power problem occurs where the power is not killed. That would be fine if GM offered the nylon gears for sale but they don't. Since your only choice is to replace the motor or use the brass gears AND there has not been a history of problems with the motors not stopping, the brass gear is the more practical route to go.