Hi DA, just noticed your post.
1. At a higher TAS there is a greater column of air flowing through the engine per time.
This is the statement where I am struggling. My understanding is that despite the higher TAS, there ISN'T actually the equivalent of any more air flowing through the engine. In 10 seconds of flight, there is the equivalent of 10 seconds of the CAS/IAS air passing through the engine. In my understanding, (which I'm sure IS wrong!) TAS irrelevant.
You are probably right. I just cannot see it. Asked a couple of friends who fly A320s and 737s, and they scratched their heads. "It's all auto throttle.... Not sure..."!!!!!!!!!!!!!!