The reason high CR is more fuel efficient is because the charge is expanded more (and cooled more) before going out the exhaust... meaning you've taken more energy out of it.
Is this where a turbo gets its rotational drive ratio from...from non-fully-expanded exhaust gas? In other words, the turbo is not driven by the exhaust stroke piston "pushing" exhaust through it bu rather from said exhaust expanding further/fully and flowing through it (the turbo)?