Boeing FBW Thrust Control not Integrated with Path Control
Unfortunately the historic separation between flight control surface control and engine control on Boeing commercial airplanes has carried over into the FBW era. As such, it is unlikely that thrust control specifically designed to provide pitch control will be coming any time soon.
As noted in entries above, the pitch axis maneuver augmentation provided by C* and C*U control laws treats pitch disturbances generated by thrust changes as a disturbance and uses the elevators and horizontal stabilizer to compensate without need for any pilot input. The relatively low bandwidth (i.e., slow acting) nature of thrust changes allows for the C* and C*U systems to very effectively counter thrust pitching moments via integral feedback control.
As long as commercial transport pitch control systems are designed such that loss of adequate pitch control is extremely improbable, I doubt that there will be any value seen in designing engine controls in such a manner as to provide backup pitch control.