Hello all, and Season's Greetings to you.
Why do we compress? To make the engine more powerful.
I'd agree with that in principle. It allows useful work to be extracted over a wide range of conditions.
If you look beyond the cycle itself to the combustion process then the picture changes because you can increase the speed of combustion by increasing the temperature and pressure in the combustion chamber.
This is misleading. You can't increase the speed of the combustion reaction to extract more energy - we've been over this before. Please see post #70. I'll repost the question I posed for you below so you don't ignore it again, and you can consider them turbine engines (this will prevent you bringing in your multiple false arguments again.
Consider two identical TURBINE engines, same size, same fuel flow, same RPM, same EVERYTHING - except one has a higher compression ratio - why is the one with higher compression getting more energy out of the same fuel?