I definitely can see the trade-off in teaching the more etymological meanings to understand how the character functions in forming compound words. Still, with such common gramatical characters I still find it distracting to be learning a different meaning and pronunciation as the one you’re seeing all the time, especially in the beginning.
Personally, I don’t see why not teach a primary meaning along with its alternative meanings and later on teach words (or short phrases) that use both. That’s how WaniKani handles kanji with multiple meanings (granted, the problem with basic grammar is way smaller as most of the grammar is made with hiragana). For example, today I unlocked 本人 (“Yourself”) and I feel it would make more sense to learn it from the meaning of “originl” than “book”. Learning these different words from different meanings would help understand the character better to me.