Every culture has a different approach to teaching music. In western nations, there (at least in many traditions) is an emphasis on learning music notation, in turn building sight-reading abilities (which for many performers is an essential attribute to have for auditions). In other parts of the world, such as India and West Africa, there is more of an emphasis on oral tradition (training the musician through example) thus building their ear recognition abilities. Is there an advantage to either system? There have been many arguments for many years regarding this issue, and I honestly believe it depends on the situation.
Music notation’s advantage is that it allows the composer to not risk forgetting their ideas. It also allows for a mass ensemble to sight read through music quickly, thus effectively utilizing the meeting time in a succinct way.
Oral tradition’s advantage is that it allows for more expression on the part of the musician. With oral tradition, the musician rarely plays the same song in the same manner twice, adding unique embellishments to the melodic lines.
It is truly difficult to say which method is better, as at the heart of this topic is specific cultural practices that have been followed for centuries. Hindustani classical music (classical music from North India) has always taught musicians through oral tradition, as it serves a purpose. In traditional Hindustani performance, there are specific sections (most notably the opening unmetered Alap section) that serve as improvisation for developing the raga (or scale). Looking at another tradition that I actually play, that is classical Arabic music, oral tradition is practiced so that the musician absorbs the maqamat (or scales) into their soul. What results is emotional playing in both the fixed melodic sections, as well as the improvisation sections known as the taqasim (in many ways these sections show the skill of the performer in question).
With western music, you do see improvisation (in styles such as jazz and rock), but in those same traditions there is an emphasis as well, even if it is just initially, on music notation (whether it is tablature or lead sheets). Of course where notation is most ardently followed is in western classical music, where improvisation is frowned upon as there is an emphasis on following exactly what composers notated. The use of music notation in the west is, yet again, the result of years of tradition.
When you are dealing with tradition, it really becomes a slippery slope to attempt critique, as many decisions of tradition are relative to your perspective. I see advantages to both systems, and to students of music in the west I strongly encourage immersion in both practices, as the mark of a great performer is versatility. Embrace every practice that music has given us, in every unique cultural perspective, as no one culture has all of the answers musically. This should be encouraging to those who study music, as there are always fresh and brilliant ways of viewing this art that has existed for a long time.