In some ways the cut root acts like a somatic seed, providing nutrients while the new plant grows out and establishes itself.
Well there you go. I think I already said that too.
Edit: I have a little more time now that I'm back so.....
Question, Does the root lose its hairs because it has been removed from the plant or because of the handling?
It's not just keeping itself static, it is generating a new plant (or more).
I have found that around 1.5" is a good size for root cuttings. I've only ever used the technique on D. regia.
I find it interesting that a root that is behaving like a root ie, supplying sustenamce should suddenly be described as being like a seed.
It's like a bald parent who is sustaining his/her (women can go bald too) offspring using money out of the bank rather than from earnings. The money is just as good no matter where it came from.
A root supplies sustenance to the plant, this damaged one is doing exactly the same only it's drawing the nutrients from a reserve. I see no reason to stop saying
it's a root
If it looks like a root, acts like a root, smells like a root it's a
ROOT