Your confusion might well come from tackling two subjects at the same time: CS props and increasing altitude. I already tried to separate them, for clarity's sake and also because CSP's are not my cup of tea.
Your fuel system, whether carburettor or injection, adds the appropriate amount of fuel to whatever quantity of air available, creating an optimal mixture for the given conditions. That's why carburettors have a mixture regulator knob.
At increasing altitude, the air becomes thinner, so the same volume of air contains less molecules.Thus, less air, or rather less air/fuel mixture, will be available to be sucked into the cylinders at each inlet stroke. Weightwise, that is. Opening the throttle will allow a larger part of the available mixture to enter the engine, but it will not increase the availability. To make things worse, a non-turbo engine relies on ambient pressure alone to pushload the mixture into the cylinders; with increasing altitude there will be less atmospheric pressure, hence poorer loading.
Again, I am not saying anything about prop behaviour. All I said equally applies to vehicle and stationary engines. If you have driven several generations of mid-to-heavy weight vehicles at high altitudes, you will have had occasion to appreciate the advantages of turbo loading.
HTH,