Just speed read this... strewth, talk about handbags at dawn!!
I'm surprised no-one has yet mentioned expansion ratio, rather than compression ratio (at least I don't think it was mentioned). The work output comes from the expansion of the gases, not the compression. A higher CR provides more expansion of the gases after combustion, which is an explanation for the lower EGT of a high CR engine.
The disadvantage of the use of a very high CR is the instability of the fuel/air mix as the peak cylinder temperature increases beyond a critical level, depending on which fuel is being burned. Detonation can occur if this is too high, which results in a "kick" to the piston, rather than a controlled push.
Talking of which, Slippery Pete wrote:
the ignition timing is simply adjusted to ensure the maximum pressure in the cylinder is occuring at TDC.
Yes, this is incorrect. It would have been more accurate to say that peak cylinder pressure should occur just after TDC, about 17 degrees ATDC in fact. This is for geometric reasons of the conrod pushing round the crank in the most efficient way.