It's not only about the fuel/detonation issue, although it is definitely important on a street/octane-challenged engine. The engine will make more power because it will need less spark advance (because of the extra turbulence during the burn caused by the squish). That means that there is less negative work - the piston doesn't see as much cylinder pressure before TDC. The quicker the burn, the less advance the engine needs and so less power is taken away from the output.

This is SOP on racing engines where the octane level of the fuel is not an issue - maximum power output is.