Some genres, like rock and folk music, involve little or no written material. There are certainly players who have never read music from a sheet. I attend a week-long folk music camp every summer, and there's no sheet music. I perform jazz "standards" in small ensemble settings entirely by ear.
But I also belong to a 19-piece jazz ensemble, that plays from sheet music. It's really not practical to expect the players to figure out their parts by ear and perform them from memory. Requiring that would greatly reduce the scope of our repertoire, and the band's ability to attract players. Sheet music literally expands the artistic palette of the composer, to the delight of both the performers and the audience.
Sheet music allows students to study and work through a large amount of literature, quickly. My kids are both studying music in college, and the amount of material they're exposed to every week is mind blowing, in lessons, class, rehearsals, and even getting together to play for fun.
Having been a part time working musician for a few decades, I've also noticed that sheet music is a band management tool. My band would be incapable of performing if we couldn't call in one or two substitutes per performance, some of whom are sight-reading on the bandstand. Same deal for a classical orchestra. In a smaller band that I play in, the bandleader is composing most of the material, and we scribble edits and rehearsal notes in our parts as we collaborate on refining each piece.
Up through the 1960s or 70s, the instrumental parts for most popular music was recorded by professional musicians who were working from written material, even if they made sometimes dramatic changes to the songs. This was just the most efficient way to manage a studio date. The touring musicians could always learn the songs by ear later on. There are stories of bands, where the first few dates of each tour still sounded rough as the band was coming up to speed on material that had already been professionally recorded.
An amusing bit of reverse psychology, the kids who learn to read can begin to have more fun on their own than just playing the boring stuff from their lessons. This motivated both of my kids.
These days, the person who is utterly helpless without a sheet in front of them is a rare exception, except maybe on piano. But there are two things "wrong" with the piano: Not just the notation, but the focus on playing it as a solo instrument. In my view, in addition to reading and ear training, the other component that needs to be started as young as possible is playing with other people. The Suzuki method does emphasize this quite heavily. It's hard to do with pianos.
I do also think that some education philosophies focus too much on notation, but being illiterate (as in: not being able to read musical notation) is restricting quite a lot what you can do and how you can learn.
I'm personally envious of those who can play by ear but have found reading music to be easier to learn by comparison and more precise.
You develop a reflexive connection between your ears and your hands, so the signals flow through your spinal cord and reptilian brain, while you're thinking consciously about the higher levels of musical structure and what's going on around you.