It is all about thermodynamic efficiency
My vote is with SP. Assuming that the OP's question could be rephrased as "why is compression desirable" or more accurately "why does engine efficiency increase with compression ratio (or pressure ratio for turbines)". The answer is that compression causes an increase in the thermodynamic efficiency of the engine. Compression causes a temperature increase of the working fluid (gas). This results in the heat charge (combustion) being introduced at a higher temperature. The result is an increase in thermodynamic efficiency.
So the answer to the OPs question is that compression results in higher thermodynamic efficiency. Everything else is fluff...