A 777 engine is actually far more fuel efficient than a rocket engine. Take a look at specific impulse [0] for different engine types. A rocket is optimised to be very light and to use its own oxygen supply. A normal jet engine can be heavier and use the air as an oxidizer. Much more efficient for power production in a CCGT.
Rocket engines are actually very efficient, especially in vacuum. Very high expansion ratios can be achieved that converts almost all the heat into jet kinetic energy.
