You can watch a Shakespeare play or you can read it.

Depending on the actors, you maybe get more out of it by seeing it or possibly more by reading.

With music and saxophonists, what you get from listening and learning by ear depends on to whom it is you listen.

With written music, the notes and rhythms vary in accuracy to the real music.

There have been many musical masterpieces that were written.  You can literally see the works of Mozart, Beethoven, Bach from the classical side.  In that case, the music is interpreted from what has been preserved.

The act of writing also implies a great deal of time spent, especially on the revision process.

So written music can be cleaner in some senses than improvised music.

Hearing music is closer to being ‘music’ itself if it is played well.

When you learn a language, you’ll become fluent by actually speaking it and interacting with native speakers.  In preparation and in learning how to write yourself, using books and written materials is crucial.

So a saxophone player who only learned from sheet music may sound stiff and predictable.

A saxophone player who only learned by ear may sound less refined and will not be able to write their own music.

You should take both approaches to reach the sound you want on saxophone!