Was Inverse Variance Weighting Really Not Proved Until Recently, Or Was A Proof Just Not Written Down?

Recently I tried to review the foundations of inverse variance weighting, but I found only Shahar's paper from 2017 which states:

 If the variances of the individual estimators are given, the ideal weights have long been known to be the inverse of the variance. Nonetheless, I have not found a formal proof of this result in the literature. In this article, I provide three different proofs of the ideal weights.

I haven't taken a formal stats course, so I'm wondering how this principle has been taught -- was a proof given as lore but not published, or omitted entirely? I can imagine it being worked out in lectures or textbooks, but I haven't found any notes.