Sample rate has nothing to do with headroom. Bitrate does.
Sample rate defines the highest frequency possible to be represented, which is theoretically half the sample rate. For e.g., 44.1kHz can only reproduce as high as 22.05kHz. In reality, the source is filtered way below that to avoid aliasing, the same phenomenon found in video where the wheels of a car appear to be going backward. In audio, this is represented by ultra low nasty frequencies.
Bitrate defines the number of volume levels represented. For e.g., 1 bit audio would contain zero dynamics. Either full volume or silence. A 2bit converter produce 3 volume levels or silence. The noise floor would be very nearly as loud as the material.
Compare those to 16bit - 65,536 levels.
24bit - 16,777,216 levels, which is 256 times more granular (headroom) than 16bit!
Though 16bit audio is quite sufficient for human psychoacoustics (the smallest difference in volume that the human brain can discern), mixing 16bit audio files, where most are attenuated, thus not achieving their full dynamic range, results in a mixed audio file way below 16bit. No one mixes a project where all tracks are placed at 0db nominal level, the only way to maintain a 16bit mixed audio file from 16bit audio tracks.
Hence the value of 24bit audio files.
Sorry for some of the irrelevant info - just wanted to give a fuller picture of the subject.
