The late Daniel H. H. Ingalls, in his book of translation Sanskrit Poetry from Vidyākara's “Treasury”, touches on this matter in his introduction. Although he is talking about Sanskrit for English readers, I find such statements useful in telling those who know Sanskrit something about English (or at least its speakers):
Sanskrit not only has an enormous vocabulary; it has also a larger choice of synonyms than any other language I know. In a natural language there are probably no synonyms. Of course, one can go to a thesaurus and find what are called synonyms. For the English word ‘house’ one may find ‘dwelling,’ ‘residence,’ ‘tenement,’ ‘abode,’ and so on. But these are not true synonyms as one can see the moment one tries to interchange them. One cannot say of the Vanderbilts that they lived in a large tenement in Newport, Rhode Island. Each word in English has connotations that it cannot shed and that permit it to be used only in an appropriate social and emotional setting. There is even a genre of English humor, perhaps best exemplified by S. J. Perelman, which gains its effect by dropping words into a setting which cries out, so to speak, against their connotations. This form of humor was never developed beyond a rudimentary stage in Sanskrit, for while Sanskrit distinguishes, it is true, between poetic words and matter-of-fact words, it achieves within each of these categories an extraordinary degree of synonymity. The poetic words for house in Sanskrit—and Sanskrit has far more words for this object than English—differ chiefly in sound and etymology. They are not bound to a particular social or emotional situation. Thus, veśman is literally the place where one enters, sadman the place where one sits down, vastya the place where one dwells, nilaya and ālaya the place where one alights or comes to rest. These words are far more interchangeable than the English ones. Nilaya will do for the dwelling of a king or a farmer or a crow.
In the context that surrounds these words, he attributes this difference (English doesn't have true synonyms, Sanskrit has true synonyms) to the fact that Sanskrit was used in an “educated” setting and was thus not a “natural” language: he thinks that it is Sanskrit that is odd here by having true synonyms, because “natural” languages never do. (He may touch on similar matters in his Some Problems in the Translation of Sanskrit Poetry; I'll have to reread it.)
Of course, everyone likely finds their own language and culture natural, and considers deviations from that “norm” as needing explanation. My personal experience, with a different Indian language (and from a different language family) than the OP’s, is that even “natural” languages do indeed have at least occasional synonyms with no difference in meaning or social/emotional connotation.
Either way, I find it informative that (at least some) people from an Anglophone culture consider it natural for there to exist no true synonyms. I hope that answers your question!