I'm afraid it's a lot worse than that. Using the top 4-6 bits would mean the material has got 24 to 36dB of dynamic range since each bit is roughly equal to 6dB of DR. You will be hard pressed to find this in even the most dynamic material. Sadly, most modern pop music has anywhere from 3 to 6 dB of dynamic range, and less! This would mean this music is utilizing only the top bit. And yes, I said BIT. ONE.
Cheers