I am wondering the original motivation for considering cyclotomic units. Maybe one can rephrase the question as:

- Why did people initially consider such units in $\mathbb{Q}(\zeta_p)$ specially?

There are many interesting results we can get with the notion of cyclotomic units, for example, comparison between the class number and the index of the subgroup of cyclotomic units. However, I think that they are not the philosophical origin of cyclotomic units. One another but stupid rephrase of the question is:

- Why was the name
*cyclotomic*taken only for such units, not for every unit in $\mathbb{Q}(\zeta_p)$?