hawk37, This is one where we can really get down to semantics. The Power Vs Thrust arguments on these forums go on endlessly, when someone can show me a diagram of the forces affecting flight (Thrust, Drag, Lift, and Weight) that includes Power, I'll surrender. For the jet aircraft (which this topic is all about), Power is only looked at as an abstract in examining Rate of Climb, at all other times direct reference to Thrust applies.
You did mention "added kinetic energy (of the air accelerated backwards), and heat energy (pardon the poor term) of the air and perhaps tires/brakes, hence the presence of power produced by the aircraft", well the air accelerated backwards is what produced the Thrust, which the aircraft requires. With respect to Noise, heat generated etc., note again the formula that I posted refers to Ta, the "a" implies AVAILABLE after all other losses.
Mark 1, as Power is the rate of doing Work, could your statement "but it is now working and generating power" be re-written, by substitution, as "but it is now working and generating a rate of doing work".
We have been raised in the mechanical era where we have an early association with Power in motor vehicles. Motor vehicles need Power to generate Torque to turn the wheels, Propeller aeroplanes need Power to produce Thrust via their propellers, so do ships. Jet aircraft skip the transformation process by directly producing thrust.
And why do ships and aeroplanes convert their Power to Thrust? - because they need Thrust, not Power, to function.
If these words can't convince you, then allow me to finish with a direct unmodified quote from the Performance Engineering text book of the world's second oldest airline (QANTAS), maybe KLM (the oldest) sees it differently -
"The output of the jet engine (including fan jet) is thrust. There is no place to measure or observe horsepower. Power is transmitted by shafts from turbines to the compressors (and to fan where employed); incidentally the energy absorbed by the compressors far exceeds the useful output of the engine. The useful output is thrust (and that's what we want), so it is useless from any technical viewpoint to go backwards to figure out horsepower".
Regards,
Old Smokey