Quintilian, in The Orator's Education (1.1), writes at some length about teaching children, in particular children under the age of seven, how to read.
He feels that they should learn to recognise the shapes of letters as well as their names and, to this end, he recommends they use ivory letter-shapes (eburneas litterarum formas) or anything they enjoy looking at and handling and naming.
Once they have mastered letters, they should then learn syllables, and this by drill. Further, Quintilian emphasises that syllables should be learnt before words, and before reading proper:
Quin immo ne primae quidem memoriae temere credendum: repetere et diu inculcare fuerit utilius, et in lectione quoque non properare ad
continuandam eam vel adcelerandam, nisi cum inoffensa atque indubitata
litterarum inter se coniunctio suppeditare sine ulla cogitandi saltem
mora poterit. Tunc ipsis syllabis verba complecti et his sermonem
conectere incipiat ...
We must beware also of trusting the first memory too readily: it is
better to have repeated syllable-drill over a long period, and not be
in a hurry to achieve continuity or speed in reading either, unless
the sequences of letters are produced without hesitation or doubt, and
anyway without the child having to stop and think. Only then let him
begin to construct words with the syllables themselves and form
connected sentences with the words.
The next step is to then start teaching the child vocabulary. This can be done by giving them sentences to copy (preferably with a moral lesson therein) and also to have them learn the sayings of famous men and selected passages from the poets because, Quintilian tells us, children quite enjoy this:
Etiam dicta clarorum virorum et electos ex poetis maxime (namque eorum cognitio parvis gratior est) locos ediscere inter lusum licet.
The child may also be allowed to learn, as a game, the sayings of
famous men and especially selected passages from the poets (which
children particularly like to know).
I think that this all indicates an understanding of the learning needs of a child. Quintilian notes too that it is best to keep things fun, make learning a game, praise the child often, and perhaps add an element of competition to the tasks to motivate them.
He also gives hints of learning materials adapted for children learning to read - the ivory letters to play with, syllable drills, and excerpts from the poets. However, it's not clear that this would necessarily lead to a market for children's books as such. Syllable drills and the dicta of famous men could easily be devised by an individual tutor.
Additionally, for all his understanding of the child, the methods Quintilian describes seem to favour a rote-learning approach - repetere et diu inculcare - and memorisation is a big part of learning to read: Ingenii signum in parvis praecipuum memoria est / In children, the principal sign of talent is memory (1.3). And so it's not clear that stories written for children to practice (and enjoy) reading would have been deemed necessary.