I have encountered beginner adults who have not learned how to read notes. Some learned through youtubes, websites, and some have only taken a one credit class in music theory, from the very basic staff to the major scale. Many have great ears. One of my adult students picked up "Girl with the flaxen hair" Debussy prelude by ear.
In the history of mankind, when oral traditions were replaced by written ones, orators gave way to scribes. Yet back then, the Greek written words had no space between them. Written texts were merely used to remind readers what they already heard. Learning was dependent on comprehension and memory.
Music notation started in the same way, from imprecise neumes in Gregorian chants to overly prescribed articulation, dynamic and pacing symbols. As humans controlled more and more the environment, they specialized, and interpreters were separated from composers. We now rely on someone else playing the music for us to listen to, because they are "experts." Performers rely on someone writing the music to play. Learners rely on their eyes before their ears, because publishers are the "experts."
Charles Hicks in the 1980s published in the Music Educator's Journal "Sound before Sight, strategies for teaching music reading."
The advice is logical, it emphasized continuity, repetition, repeated patterns, narrow range and same key signature. It's a constructivist approach. His recommendation was to explore the PRINCIPLES of notation rather than the SYSTEM of notation.
Hidden in the writing of symbols are organized SOUND. If one can help a student first notice how sound perception can be organized (in time, in pitch in volume, in attack, or in structure) before one introduces them to the written notation, it would help contextualize the purpose of learning the symbols. For example, this is double slower, or double faster. This is getting gradually slower versus this is a change of speed.
Babies learn to talk by imitation. Why should one learn written music before one learns musicianship? how to feel a regular beat, an upbeat, or a syncopation; what is the difference between a feel of two - or three? how to recognize the feel of a sad mode- or a happy mode? how to slow down or accelerate in gesture?
Our music education system puts a lot of weight on the Oral, less on the Aural tradition; it is leaned toward the visual rather than the audio part of learning music. Folk or Art music around the world are, for the most part, still transmitted by oral tradition.
In these traditions, even when written down, learning music required close encounter with an instructor, because learning is through exposure, enculturation and imitation. In India, a novice just listens for a year before attempting to improvise lightly a scale (raga). Years can pass before he or she is allowed to imitate licks of the teacher. Here in the U.S., there are students who, after 5 to 7 years of lessons and practice, get technically proficient but barely go to one concert a year.
With certain instrument, such as the trumpet, hearing the sound is extremely important as the same buttons may be pressed, but the way one blows determines the pitch. In order to know whether or not one has blown the right pitch, one has to hear it first.
Why don't we learn piano the same way? Less like a typewriter, more like a musical instrument.
How many of us teachers have encountered a student that played Ode to Joy with the dotted quarter note - eighth note instead of the written quarter notes? They are guided by what they hear on the inside. Most beginner piano books start with what they consider standard repertoire that everyone should know, such as Mary had a little lamb, Jingle bell and so forth. But they publishers changed the rhythm! This repertoire is also not updated nor culturally relevant. The Mexican Hat is not what Mexican Americans listened to, and not all of us know "Oh When the Saints" or Dvorak's symphony, but many will know the latest Lady Gaga, Pentatonix or Disney movie. If the point is to teach something familiar and already in students' ears, then we need an online continuously updated book for the younger generation. One where they can go in and choose songs they know, arranged for different levels, and print out song by song as they progress and taste changes.
As for the different types of arrangements one can do for each song with a chord chart, this can be learned in workshops, webinars, or online conferences. Technology can be used to bring the music learning methods to the 21st century.