Does literacy remove your ability to be a bard as good as Homer?

There's a thing in our very literate modern society which still survives following more or less the same pattern: jokes (and the longer ones in particular).

Think about it: even if you can easily find printed books full of jokes, in practice jokes are mostly an oral thing. You tell one to a friend, who in turn tells it to another friend, and so on. But unless the joke is a single sentence, at every step in the chain it will be distorted and retold a bit, even if it remains recognizably the same joke (for some people, adding a lot more words to the original version is also not uncommon). Nobody is expected to remember a joke word-by-word, and even the same person telling the same joke twice will probably not use the very same words. Yet it will be the same joke.

Maybe being a guslar is not so different from telling a joke 2294 lines long. Note also that "being able to repeat a joke non-exactly after hearing it once" is not considered difficult, even if the joke is 200+ words long (while "being able to repeat 200 words exactly" is basically impossible for the average person).

What do you mean by them memorizing the songs, if they don't repeat them word for word? Do you only require that all the events in the version they heard happen again in the version they sing? Are there audio recordings of their singing? Those should help reduce confusion here.

Is there a reason I should want to? I mean that sincerely. Is there a reason I should want to memorize a specific handful of books' worth of information? Because rather than memorize a few thousand pages designed to be memorizable, what I've actually done is read/hear hundreds of thousands, mostly likely millions, of pages or their equivalent, with hundreds of new pages per day added, and extracted the key insights as best I can while keeping track as best I can of where I got them and how they all fit together.

I've read or heard or watched the Iliad and Odyssey, Plato, Aristotle, the Oresteia, the Bacchae, and thousands of other books, plays, songs, movies, shows, lectures, podcasts, etc. Would anything about me be better if I'd instead memorized the Catalogue of Ships or the exact text of Plato's Crito and Apology? 

Memory needs to be developed. The ability to develop memory didn't disappear with the advent of writing, though some of the motivation may have. Still, the ancient Greeks and Romans developed a technique for memorizing long strings of pretty much anything. It's generally known as the method of loci and it continues in use to this day.  Here's the opening of the Wikipedia entry:

The method of loci is a strategy for memory enhancement, which uses visualizations of familiar spatial environments in order to enhance the recall of information. The method of loci is also known as the memory journey, memory palace, journey method, memory spaces, or mind palace technique. This method is a mnemonic device adopted in ancient Roman and Greek rhetorical treatises (in the anonymous Rhetorica ad Herennium, Cicero's De Oratore, and Quintilian's Institutio Oratoria). Many memory contest champions report using this technique to recall faces, digits, and lists of words.

Then:

John O'Keefe and Lynn Nadel refer to:

... "the method of loci", an imaginal technique known to the ancient Greeks and Romans and described by Yates (1966) in her book The Art of Memory as well as by Luria (1969). In this technique the subject memorizes the layout of some building, or the arrangement of shops on a street, or any geographical entity which is composed of a number of discrete loci. When desiring to remember a set of items the subject 'walks' through these loci in their imagination and commits an item to each one by forming an image between the item and any feature of that locus. Retrieval of items is achieved by 'walking' through the loci, allowing the latter to activate the desired items. The efficacy of this technique has been well established (Ross and Lawrence 1968, Crovitz 1969, 1971, Briggs, Hawkins and Crovitz 1970, Lea 1975), as is the minimal interference seen with its use.

If you're curious psychologist David Rubin has written Memory in Oral Traditions: The Cognitive Psychology of Epic, Ballads, and Counting-out Rhymes (Oxford UP 1995).

We're witnessing a similar change in our time. Many people today think that reading books is difficult and impressive, when 20-30 years ago everyone was reading books easily for fun.

A similar thing is happening with music: people are losing the ability to enjoy instrumental music. Instrumental songs almost never chart today, compared to the 60s and 70s. People do listen to soundtracks from movies and games, but that's a borrowed emotional effect.

I haven't checked, but willing to bet that people's ability to navigate without an electronic map is also pretty much gone.

How does this compare to freestyle rapping? While freestyle raps are certainly not the same length of these epics, the ability to compose (and then recall) verses composed on the fly would seem comparable. It seems like a compelling comparison especially in light of the proliferation of hip-hop and it's integration into online spaces.

A few other questions about these Yugoslavian Epics comes to mind: How much redundancy is there? How many plot-holes or continuity errors are there (akin to Homeric Nods)? How many divergent narrative threads are there?

Would I be right to assume that if the poet can recite their poem again but retaining the same plot holes and discursions that it indicates a superior memory? If they are using a template or formula to create these discursions why wouldn't they tend to "correct" plot holes or produce different discursions each time? Standup comedians may repeat routines thousands of times, but especially for more improvisational comics like Robin Williams or Gilbert Gottfried you would be hard pressed to find two exactly alike, and like these bards they are entertainers.  

Been doing this. Reading less. Writing a LOT less. Memory has improved a lot.