I found this link which lists 12 compound tenses like future perfect, along with some other outlandish forms like perfect imperative (brr), further to the normal as–is–os. Are they used in anything than perhaps literal translations of texts from other languages? It feels like they are defeating the simplicity principle which makes Esperanto so elegant. To my best knowledge (and background from my own language), it's possible to express any other tense than present or future or past by words like ĵus, I have yet to see a counterexample.
Even though it may seem like the compound tenses only add difficulty to the language, they do have many advantages. They are useful in literature, like you mention, but not only translated works, also originals. Below I listed some quotes from a magazine. I'd say that compound tenses are less common in spoken Esperanto, but far from non-existing.
One can use the compound tenses to express complex situations and also add variety to the writing. It might be possible to rewrite such sentences using the simple verb forms and other words like ĵus, but I think it is simpler to use the compound tenses.
The passive participle is often used in a way that leaves out a subject otherwise necessary. This is very common also in when speaking.
La pordo estas ŝlosita.
Post 30 jaroj televidiloj ne plu estos uzataj.
Ŝi estis tre konata en Brazilio.
In the last issue of the online magazine Umujo compound tenses appear 13 times.
- Perfect: 1
- Progressive present: 1
- Perfect: 5
- Progressive present: 4
- Future perfect: 1
- Perfect infinitive: 1
I picked out some examples:
Ni volas helpi ĉiujn lingvojn, sendepende ĉu ili estas gigantaj, minoritataj aŭ kreitaj.
Italoj estas multe konataj eksterlande por esti tre gestemaj.
Li estas preskaŭ mortinta, kaj ne diros ion plu.
Ni seniluziigos nian ĉefaron kaj estos maldungitaj.
Ĝis nun mi estas laboranta, konsiderante ĉiujn filmetojn parto de sama rakonto.
You will find people who stand by the "complex tenses." (It's likely that a few will answer here.) The point of Esperanto is to be simple, and it's possible (and encouraged) to express any thought with the basic -as, -is, and -os. If the timing of the event needs to be clarified, it can be clarified by additional words.
Participles are best thought of as adjectives. Adjectives can be combined with estas like this.
- Jen verda arbo.
- La arbo estas verda.
Participles can be treated the same way.
- Jen falinta arbo.
- La arbo estas falinta.
It's very tempting to see this last sentence as "the tree has fallen", but I like to encourage people to see it as "the tree is a fallen one" (it is a tree in the state of being fallen.)
So, yes, the "complex tenses" are used, but it's worth considering whether the people are using them are really embracing how Esperanto works or just carrying over bias from their national language.
The compound tenses follow directly from allowing participles to bear tenses. The names that are shown on that website are borrowed from the grammars of other languages (and some of them are not just dubiously chosen, but misspelt).
You are not obliged to use compounds, but they aren't any more conceptually complicated than relative time itself. Without them, one would just have to express the same ideas in a haphazard way with adverbs and particles. In other words, a regular system would be replaced with an irregular system, without any gain other than a very superficial simplification in appearances.
(Concerning the compounds with -u)
The names given are misleading; the -u ending is not just used for the imperative; it is a "general deontic mood" expressing wishes and ideals. So, it is possible to construct examples in which it makes sense:
- Estu travivinta tian malagrablaĵon por la lasta fojo! May you have experienced such unpleasantness for the last time!
- Ne estu malvenkinta... [muttered, opening the sports section of the newspaper] Don't have lost...