In Spanish, there are a few tenses that exist but are almost never used in daily life, like the subjunctive future and future perfect tenses. They are only utilized in legal documents and older pieces of literature.
Question: Why are these inflections still recognized as tenses of present-day languages, when meaning can be conveyed with or without those tenses? Why are they still classified in a way which makes it seem like they still have currency?
As far as I know, every language has forms of expression specific of the written/formal language. Actually, I would say that in spanish the spoken language is slightly closer to the written language than in many other european languages. As for the examples you mention:
-It is not true that the perfect future is not used. As a native speaker I can tell you that it is widely used. Example: "Para cuando llegues ya habremos terminado de cenar" it is a perfectly normal sentence , which doesn't sound far-fetched or anything like that and which makes a crucial use of the perfect future in the first person (plural) ("habremos terminado" = "we will have finished", literally)
-The future subjuctive: It is true that it is not very common, BUT, as you mention, it is common to find it in written language and also in some sayings and expressions in the spoken language. For example, "donde fueres haz lo que vieres"(equivalent of the english saying "when in Rome do as the romans") or similar constructions. I would say the future subjuctive is common enough and useful enough so that calling it obsolete makes no sense.
An interesting example, however, is how the imperfect and perfect simple subjuctive past tenses of latin merged into one single tense in spanish, thus making the two forms "fueras" and "fueses" equivalent. In this case spanish DID lose something, namely, the perfective aspect of the simple subjuctive past, whose role can be played by either its imperfective counterpart or the subjuctive pluscuamperfect ("hubiese sido"), both very common in conditional constructions.
Because language changes gradually.
So for some features (in this case the mentioned Spanish tenses) there is first some alternative to express them, and this alternative becomes more frequent than the old form over time, until the old form sounds bookish and archaic or even obsolete. In the final step, the old form is no longer available and sounds ungrammatical.
Classification has nothing to do with frequency of use. Even if they are only rarely employed in restricted formal contexts, they remain tenses.
Spanish does not have obsolete tenses except the future subjunctive which is not particularly worthy of note (its almost identical to the past subjunctive with a vowel switch).
In fact, I would go as far as saying that Spanish uses all of its tenses quite profusely - unlike French, Italian where there are quite a number of tenses which are semi-obsolete and native speakers struggle with. In spoken French even the simple past is quite rare, let alone the past subjunctive.
What Spanish does have, is lots of second language speakers who are not comfortable with all of the language's tenses - which is precisely what makes them instantly recognizable as second language speakers.
