I don't think that's quite right Rob - in terms of "A better explosion" - 'better' is a bit short on specific meaning and actually in a petrol engine there shouldn't be an explosion.There's combustion (and it's not the same.)Why does a powerful engine need a high CR?
To get a high Compression and a better explosion.
A diesel wouldn't work at a low CR because it needs the Compression pressure to generate heat (like the bike pump does in your hand) to ignite the fuel.
The reason higher compression is better is not about the burn being better, it's about the gas expansion extracting more heat - that wikipedia article explained this well I think.