Learn English – Short expression to convey “but consider the source”

Yes: the root is ultmately rogare, "ask".

Interrogative: asking at intervals, or between people.

Prerogative: this comes from Latin, "to be asked first" and connotes privilege.

Derogative: this means partial abrogation. Abrogation comes directly from a Latin root abrogare "to repeal, to disregard, ignore, repudiate, to cancel, revoke, to take away" (OED). This is how [for example] the UK can implement a derogation from European Union law: it disregards the undesirable part of it.

The meaning of derogative in the sense of "belittling" is an extension of this, detracting from or disregarding reputation.

It is not in itself clearer than any of the phrases your mentioned. But it is internationally recognised and has a fixed, established meaning that everyone recognises immediately. The very fact that it is Latin alerts the reader that it is a special term with a fixed meaning, which is convenient, ceteris paribus. The same applies to other terms, such as a priori, mutatis mutandis, and alea jacta est.