"...there is no addition of heat..."
"The total enthalpy and the total temperature are constant."
I think it's fair to say that picking apart your post would not be helpful. I mean no disrespect, but you seem to stylishly increase complexity while attempting to characterize a simple concept. I prefer a straightforward characterization. This is a technical forum, and I may be out of place. I enjoy metaphor and global inference. Mathematics is like a boggy swamp when I want to blaze a hole in the ether. I get what you write; I can't be sure if your prose is proprietary, paraphrase or quote.
"We cannot use the incompressible form of Bernoullis equation across the Shock". Well, of course, that is precisely what I said.
"The density of the gas varies locally as the gas is compressed by the object." Again, intuitively (and textually) obvious.
I wouldn't correct you, what you say is enlightening and accurate, but I think you want me to be wrong, or somehow in disagreement with technical prose. Any Natural phenomenon can be explained in a number of ways, from the entry level to the arcane and hopelessly circuitous. I am not expert in aerodynamics by any means and made that clear at the beginning. I won't learn anything if I always have to be right or the most learned in the room.
Basically, I like the pictures more than the text, always have. Never grew up I guess.
All the Best (Is Australia as beautiful as I imagine it to be?)
Airfoil