As for extending the range to the full width, one has to be careful doing that on any given scene. ''Paper White' on film is usually way below 255/255/255 (in 8bit space), for example the white of the Rabbit's fur or teeth. Extra headroom is left for whiter than white, the specular highlight on a chrome car bumper, the glistening specular highlights on water droplets, headlights pointed towards camera etc.

Usually a logarithmic gamma curve is used to get the information out.

You want to stretch the range, but not too far, otherwise it all ends up flat and lifeless with no dynamics, kind of like the 'loudness wars' on CD releases these days.