The semantic error you're making is redefining the general term compression as the more specific "isentropic compression". The process by which the compression takes place is not prescribed just by the term "compression" as you did originally. Just saying "compression" specifies nothing about the process by which it happens. Compression can take place (theoretically) through an isentropic process, or a non-isentropic process, with work being done on the fluid (increasing its total enthalpy) or not.

I get your point that the shock contributes to the heating through irreversibility, and agree that has a significant impact on the sensed temperature. If we want to tie your point back to the original post, one could say that "compression and shockwaves" are the cause of re-entry heating to ensure you are explicitly capturing the effect of the shock.

Whether you consider the shock heating to merit explicit mention or whether you see it as a detail associated with the specific means of compression is largely a matter of perspective & practice.

The gasdynamic basis of shock formation is derived by considering what happens when pressure fields are no longer able to smoothly vary as the speed of a body exceeds the speed at which pressure disturbances can be communicated upstream, namely the speed of sound. The pressure jump across the shock is elemental to its derivation. Practitioners commonly view the shock as the means by which compression takes place and pressure fields reconciled. As I noted above, just saying "compression" doesn't imply "isentropic" and so the entropy-generating processes associated with a shock performing compression are viewed, for example, as thermodynamically similar to viscous heating of the fluid in a gas turbine compressor.

Consider the following extension of this thermodynamic process. The gas is shocked, and then we adiabatically expand it back to its original density.

Because entropy was added, the gas is now hotter than initially. But it is not compressed. The heating wasn't due to compression, it was due to dissipation at the shock. That dissipative process is separate from compression, and you are confusing the two.

The incoherence of your position should have been clear to you. You seem to think that compression, as a cause of heating, doesn't even have a well defined amount of heating. Your explanation isn't even wrong, it's undefined.

Well, but the gas does not reversibly expand again between the shock and the stagnation point. So clearly it is heating up, even if it were compressed isentropically.

The position is far from incoherent. Temperature rise during isentropic compression is well understood, as is the temperature rise and total pressure loss through a shock.

No, it is quite incoherent. Specifically, it fails to even offer what any physical theory must: a quantitative prediction. Compression, in your view, can be allowed to produce variable amounts of heating, for the same change in density. Since you aren't making a quantitative prediction, how is what you are saying even testable?

(The answer is that compression produces a specific amount of heating when it is adiabatic, and additional heating comes from dissipative processes that are occurring alongside the compression, but that are not themselves compression.)