What happens when you apply full throttle to the engines of a Boeing 787 at cruise altitude for 5-10 minutes?
Other than wasting fuel, what maximum speeds are reached?
Does that pose any danger or damage to the airframe?
Autopilot flying straight and level
Upon reaching the VMO/MMO the A/P will be inhibited from trimming down any further, which will result in the airplane climbing at the VMO/MMO.
Overspeed protection limits the speed to which the airplane can be trimmed. At VMO/MMO, the trim reference speed is limited by inhibiting trim in the nose down direction.
Hand flying straight and level
Pushing the thrust levers forward will result in a climb at the current speed due to the fly-by-wire design—only the trim buttons change the "trim reference speed".
Once the column forces are trimmed to zero, the airplane maintains a constant speed with no column inputs. Thrust changes result in a relatively constant indicated airspeed climb or descent.
Source: Boeing 787 FCOM chapters 4 and 9.