Efficiency and speed
I think efficiency of an engine is defined by fuel spent for unit work - in case of an aircraft that faces roughly constant drag, by fuel spent per distance covered. Not by fuel spent per unit time!
This means that at slow speed, like on takeoff or hover, the efficiency of an engine is zero. It is not getting anywhere!
Now, a jet engine works by burning fuel and accelerating the fuel and a small amount of air to a great speed.
This means that jet engines are efficient at great true airspeeds - at airspeeds comparable but lower than those of jet blast. At lower speeds, much the energy of the jet is wasted.
Incidentally, it follows that jet engines are inefficient at all subsonic speeds. However, wings are much less efficient at supersonic than subsonic speeds... so the engine/wing combination at supersonic speeds is not very much better than at high subsonic speeds.