I have never seen compression to be considered inherently reversible, certainly not in the aerospace or hypersonics/reentry communities. I assume you come from a different background?

Care to explain your second argument? Even when the density reaches a limit, the change in pressure over the shock does not, so you can pump in energy arbitrarily (of course your gas would dissociate at some point). The total pressure loss can be complete if your initial Mach number is high enough.

Let's look up a definition.

"Compression: decrease in volume of any object or substance resulting from applied stress."

Compression refers to a reduction in volume, not an increase in pressure. This is finite for gas crossing a shock, even as the mach number goes to infinity.

Exactly. There's no mention at all about the foundation of all your arguments, namely that compression be inherently isentropic. It simply is not. You can add it as an additional constraint, if you want to.

What I say is that even when dV approaches a constant, the pressure still rises, so the product also rises.

[edit: removed snark]

Requiring compression to be isentropic is just requiring "compression" to be a well-defined term with a specific quantitative result. Otherwise, it's a vague term that offers no quantitative prediction for how much heating it produces for a given change in density. That's not science.

Look, where does this idea come in that compression "as normally considered, does not generate entropy"? The inlet of a supersonic aircraft or a ramjets/scramjet performs non-isentropic (shock-based) compression. You're coming up with your own definition of compression that is inconsistent with gasdynamics practice.

Considering compression to be isentropic is just nailing down what compression means enough for its heating to be actually definable. Otherwise, the argument is just "if there's compression occurring, all the heating must be considered as being due to compression" which is just bullshit.