Why doesn't a full yoke deflection also change the stabilizer trim on the Boeing 737 MAX?
The yoke does move the elevators, whereas the trim moves the horizontal stabilizer. The stabilizer is much larger than the elevators, and therefore is more effective than the elevator at extreme angles. Even with full backpressure, the nose would continue to pitch down. 



Nonetheless, all 737NGs/MAXs have trim cutout switches, 1 for the autopilot and 1 for the normal electric trim. Using these would immediately disable the electric trim. These are generally part of a standard trim runaway situation, but the crew did not recognize the situation and failed to use them.