Wait, there are 2 different things:
Originally Posted by Willie Jan
1) You have a medium that records an image, the negative, which is very good at what it does.
2) Another medium that represents the information in the negative, the paper. This one will go from white to black within 4,5 stops of exposure. That doesn't mean you will only get 4,5 stops from the negative represented on the print.
The negative has rather low contrast, but the paper has much higher. The combination can show much more than 4,5 stops of the original scene. I've done some film testing and I can show 10 different tonal values of the original scene in a print, from absolute black, to absolute white (and a condenser enlarger). I can do this by overexposing by 1 stop and pull process accordingly. That's what I do in high contrast situations only, in cloudy days the manufacturer's recommendation is just fine. That said, it doesn't mean that the negative always prints itself, some d&b might be required to get the best result.
Now, in that specific case, if you only had 8 stops of subject brightness range, I don't think you needed to go that far. IMHO, you tried to solve a problem that didn't really exist.