That's a great point and very interesting comment. I imagine one of the reasons for this formalized (or if you don't like it, over-precise) language to arise and take hold in the Indian setting may have been the fact that Sanskrit too is capable of an amazing amount of ambiguity, in multiple ways:

1. Creative re-interpretation/re-analysis: A lot of commentators have re-interpreted existing verses to derive different meanings, and this is very possible to do. To pick a simple example, there is Kālidāsa's verse “…jagataḥ pitaru vande pārvatīparameśvarau” which clearly is a prayer to Pārvatī and Parameśvara (Shiva). But pārvatī-parameśvarau could be re-analyzed as pārvatīpa-rameśvarau (Parvati's and Ramā (Lakshmi)'s husbands), i.e. a prayer to Shiva and Vishnu. Similarly there are Shiva-para and Vishnu-para interpretations of various verses/works, people have written spiritual commentaries on love poetry, etc. So if something straightforward you say can be interpreted to have any meaning whatsoever (exaggerating a bit) by a sufficiently clever commentator, you better be careful :)

2. Happening naturally: Poets have used this too, what appear to be the same word being used in different settings. For example, here's a prayer that millions of people recite, to Ganesha: “agajānāna-padmārkaṃ gajānanam aharniśam / anekadantam bhaktānām ekadantam upāsmahe” — here the first line has the well-known word “gajānana” (the one with an elephant face), but it also starts with “agajānana” with appears to be the opposite (not an elephant face?). Actually the simple compound “agajānāna-padmārkaṃ” turns out to be made from: a-ga=mountain (that which does not move), thus agajā=daughter of the mountain (Pārvatī), agaja-ānana=Pārvati's face, agajānana-padma=the lotus of Pārvati's face, and the whole word agajānana-padma-arka=the sun to the lotus that is the face of Pārvatī (the sun of course being what makes a lotus bloom), thus it's a simple adjective describing Ganesha (namely that he makes his mother's face bloom with joy). And this is a perfectly straightforward usage of language that most educated readers will simply understand and find unremarkable, not a trick. At most a pleasing coincidence that the same syllables repeat (known as “yamaka”). In the second half, “ekadantam” refers to Ganesha having one tusk, but the “anekadantam” that it starts with is not the opposite of that but simply “anekadam taṃ” (him, who gives many things).

3. Used intentionally: At the extreme, poets have used ambiguity in the above way and also using puns (śleṣa, words with multiple meanings like kara=hand/doer/tax), to compose poems that have multiple meanings, including entire continuous works of poetry that tell two stories at once (each stanza being interpretable in two ways, and in one instance even up to six ways). There's a book about this called Extreme Poetry (https://cup.columbia.edu/book/extreme-poetry/9780231151603 — unfortunately for the lover of literature, this is a product of modern academia so heavy on theory and light on examples, but worth a look nevertheless). There's even a verse that consists of the syllable yā repeated 32 times (yāyāyāyā...) (https://www.scribd.com/document/6591853/The-Wonder-That-is-S...) which is not just “yeah, yeah” but is intended by the author to mean something. :-)