Would the use of participles be more dominant in literary work/translations, and the spoken form would be more likely to use the "efficient" form, using manĝas instead of estas manĝanta?

Joke: Mathematicians are efficient. They're so efficient, they even spell efficient efficiently. They can spell it with only four letters. L A Z Y.

It's not that the active compound (participle) tenses are more "dominant" in literary works; it's just that in a literary context, a nuance may sometimes be desired that is unimportant for spontaneous, everyday conversation.

But for the most part, including in literature, the compound tenses are just unnecessary. They are bulky and don't normally give you information that wasn't already apparent from context, or that could be clarified with a short helping word like antauxe, jam.

A concrete example:

— Bona homo, ĉu mia amiko, la nobla Vinicius, ne sendis por mi portilon? — miaj piedoj estas ŝvelintaj kaj mi ne povas iri tiel malproksimen. (from Quo Vadis?)

In spontaneous speech, I suspect most people would just say ŝvelis. I think the author chose the compound here to clarify that the feet are still swollen now. Honestly? It doesn't make a big difference.

There are very few cases I think, where a compound tense would be absolutely mandatory - maybe none at all. In some languages (like Russian), the compounds are altogether absent, yet clarity doesn't suffer. English speakers have a hard time coming to terms with that.

In English a difference in form distinguishes between the verbal and the adjectival.

My feet have swollen
My feet are swollen

In Esperanto, I am not sure that you could definitely say, Temp, that your example is a case of a complex verb form.

(I think you are right to interpret this as like saying my feet are sore - in a certain state - rather than than what your feet have been up to.)

The thing about the complex verb forms is that they are a legitimate part of Esperanto and you can use them whenever you feel that they are appropriate - even in conversation.

The English beginner, perhaps needs to reminded that their usage is different in Esperanto, which often uses a simple form where in English a compound form might be used.

But to suggest that the Esperanto compound verb forms are a feature of literary usage is to overstate the case.

Yes, sudanglo, my example was not the greatest. The problem is, I was searching through the Tekstaro for active compounds, and I was struggling to find a case where it was obvious why the author would choose the compound over the simple form.

In my experience, compounds are a little more frequent in literature than in speech. This isn't to say that you can't use them in speech, or that they're illegitimate. But given that anglophone learners have a tendency to overuse them anyway, I now prefer understating their usefulness, at least initially.

It is also possible that my Slavic intuitions make me biased against compounds. I think that to some extent usage of compounds is a matter of personal taste.

Relatedly: It would be interesting to find a context in which the compound active tense would be obligatory - e.g. the desired meaning would be totally lost without it, were it to be replaced by a simple tense. A casual look through the Tekstaro revealed no such instances.

Given the number of instances of active complex verbs in the Tekstaro, I think it is going to need more than a casual look to establish your thesis.

But in any case, what would be wrong in Esperanto offering different ways of saying the same thing.

I don't quite see why one should avoid the complex verbs to say:

You should have said
I would rather have had
I was just going to say that
I was just leaving the house when

All of which are the sort of thing one might say in conversation and all of which are naturally expressed in Esperanto with complex verbs.

Also, for example, given the range that the simple past in Esperanto covers - a single act, a repeated act, a finished act, a process, action before a past time etc, it looks unlikely that the desired nuance will always be expressable with adverbials, conjunctions, whatever.

Here's an example I like from Treasure Island (a very good read in Esperanto by the way). One of the pirates has been frightening the patrons at the Admiral Benbow with his tales.

La klientoj timiĝis plej multe pro lia rakontoj. Terure ili estis pri .......
Laŭ lia diro, li estis vivinta inter la plej malvirtaj viroj, kiujn Dio iam permesis vojaĝi sur la maro.

Antaŭe vivis, jam vivis, iam vivis don't seem quite to get it.

sudanglo:..from Treasure Island .. One of the pirates has been frightening the patrons at the Admiral Benbow with his tales.

La klientoj timiĝis plej multe pro lia rakontoj. Terure ili estis pri .......
Laŭ lia diro, li estis vivinta inter la plej malvirtaj viroj, kiujn Dio iam permesis vojaĝi sur la maro.

Antaŭe vivis, jam vivis, iam vivis don't seem quite to get it.

IMO iam vivis should be adequate if one doesn't insist on a literal translation. Many fairy stories begin Iam .. plus the use of the past tense.