Why do we compress - to release more energy to do useful work per unit time within the engine (be it piston or gas turbine).
It's so that less heat is added to the air over the entire cycle.
Burning a certain amount of fuel produces a certain amount of energy, let's call it X. You can't change the amount of energy released by burning a fuel by burning it faster or slower or under more pressure. Burn it as fast or slow or under as much pressure as you like, the amount of energy stored in that fuel is constant.
The energy produced by X is divided into waste heat, useful energy and sound by an engine. The sound is so negligible against the power output of the engine, it can be ignored.
So energy from the fuel = useful work + waste heat
The ONLY way to get more energy out of the same amount of fuel is to make less waste heat. Higher compression results in less waste heat transferred to the air by the end of the cycle.