Most likely, the noise floor was not a result of the CD medium, but of the recording equipment or ambient noise in the room where the recording was made. It is virtually certain that the noise floor was not a result of the CD format. To which specific recording were you listening?
A pretty quiet room can have 30dB of noise, so if one were playing a CD in such a room and wanted the softest possible recorded bit to be heard above that, the peak volume in the room would be 126dB, if the full dynamic range possible of the CD were used. And if that peak were maintained for very long at all, it would damage your hearing quite quickly.
See:
http://www.asha.org/public/hearing/Noise/
Basically, if you went to a symphony concert, there would be ambient noise in the room drowning out the very softest sounds on stage. If they went a full 96dB above the ambient noise for long at all, you would suffer hearing loss from it.
In other words, the dynamic range of the CD format is good enough for all practical purposes.