According to the Hobbit, the map that Gandalf gives Thorin is paper:
Gandalf: "Your father could not remember his own name when he gave me the paper, and he never told me yours; so on the whole I think I ought to be praised and thanked."
This map predates the fall of Erebor to Smaug in TA 2770.
Oh, very interesting! Because it is made to look like parchment in the movies - do not have a printed The Hobbit by hand. Is the word used not to alienate the children - the intended audience of the story? Do we have paper somewhere else in the story in the Hobbit outside of the Shire?
But could the map predate the Fall of Erebor? Smaug is drawn on it it already. The "Desolation of Smaug" is a place name placed in the centre - Dain Lord in Dale is put in past tense - "here was"?
It could have been made in exile. It was not needed before, before the Fall of Erebor a map would have shown how to get to the secret door from the inside - the knowledge how to find it from the outside has not yet been required - one just used the main door?
It was yet an emergency exit, not a possible future break-in point?
We know dwarves flew to the Blue Montains - and that way led though the Shire at some point - they very well might have drawn the map on their way on any sheet they could get hold of while their memory was still fresh?
So either the map was drawn after the Fall of Erebor or Bilbo replaced the original map in his oral deliveries of that tale (to the children - maybe even handing the modified and simplified version around) and later in book to be merely a prop/visual help for the listener/reader. If he has done so, he was not above rephrasing Gandalf's statement accordingly.
We already do know that Bilbo tampered with his story for various reasons - to enhance the performance of the tale and to contextualise it for the hobbit children I would find the most innocent of those, actually - [or having Tolkien handing the map to his own children while telling the story
].
Imho Bilbo is first and foremost an entetainer and chronicler second.
Insomuch his way of story-telling is still more audience-oriented - more "oral" - that e.g. that of Frodo or Sam.
Doesn't mean he'll have to learn to read or write! A smith might know runes, a nobleman for sure, a trader maybe, a herdsman or farmhand... i doubt it!
So we do agree here.
Hobbits write...largely genealogies. But i agree. Rohirrim do not write books. Maybe inscriptions, maybe even letters, or scrolls, but not books.They are not very learned.
Which means family trees - which means structures - which means analytic thinking how to express complex intertwined multidirectional relationships in 2D. Quite a complex task.
Remember the: "He's my second cousin once removed on his mother's side" line from the movies? This is far more reflective and requires counting the generations on a diagram than just to claim somebody to be his/her fraternal or maternal kin or "sister's daughter". It also requires the awarness that something can be viewed from multiple points of view - like the different family connections from several sides.
But constructing a text differs from mere telling - weaving - a story. A word once said is gone. You do not self-edit - you have to work with what you have said (as any adult who told an inprovised self-invented story to children will notice soon enough...
) . As such it is far more important how and when something is said that what words exactly has been used. When people start to use text they tend to pay less attention to how something is said but get fixated on the specific word they use - they start to self-edit - rephrase (the: "let me rephrase this" line) - correct - take words back - listen to oneself speaking as they would reflect on a sentence that they write - focus more on the topic than on the audience and the immidiate effect they have on their recipient. It also makes word-plays more sophisticated.
And the Rohirric nobles would for sure dictate and read letter - at least with the outer world. Would they write them by hand themselves? I think they would have scribes for that - who would also do the editing - maybe before signing one would re-read the written text to check if it was as intended and the just sign or put one's seal on it.
Hobbits also have the reputation of being simple but unlearned-but they are learned in their own ways, they write family chronicles and letters, if little else. And i doubt there are Gamgee or Roper chronicles... Took, Bagginses, Brandybuck chronicles -sure!
As I said literacy tends to "bleed down" into broader society as people tend to immitate the upper classes with time. Some - even if not all - figures of speach and elements of text-construction tend to be used also by people who whoud never construct a real text themselves. And some - who for whatever reason cannot write fluently themselves - can learn how to dictate a functional text or letter by having heard plenty of texts/letters read to them.
A 6 or 7 year old child ... that is very different from a 10 year old child or a 21 year old adult.People will,learn what they need and catch up lots of things which they are confronted with on a regular basis.
Yeah - it is usuallly considered harder to learn to read the older one gets. Beyond some very gifted individdums once this learning windows closes in childhood it becomes very difficult to become really fluent in it...
Usually one has to learn reading any language in any script untill a certain age - then the brain gets used to the concept and it is easier to learn other systems. Forcing an adolescent or older to learn to read from scratch is quite difficult for all sides involved - and in some rare cases might even be found impossible. Otherwise no one would keep to torture relatively young children with it.