Crabman: No. You have not answered the question, merely repeated it. We know there is an increase in efficiency - half the question was predicated upon that very observation.
So the answer to the OPs question is that compression results in higher thermodynamic efficiency. Everything else is fluff...
The question is why? If you read through the thread properly you will find it has been answered along with the other question posed in the OP. However, the answer slippery gave on page 1 is incorrect.