
I mean in terms of professional artists. Nearly every one of the well-known artists have been formally educated in art, and self-taught artists even today appear to be almost shunned.
The only reason this sticks out is because it’s nothing like that in similar fields…? I mean, people are acclaimed as musical geniuses without having ever stepped foot in a conservatory. People like Tolstoy and Dickens aren’t naturally expected to have studied Literature at an education institute. So why does art school almost seem like an indisputable requirement for visual artists?

1) Musical geniuses all have teachers
2) Many musicians do study music in college
3) Tolstoy and Dickens lived in a different time than we do. Also, you’ll notice most authors at least took some classes in english and that most of them were native speakers of the language they wrote in (Joseph Conrad is amazing).
4) No one really teaches art privately, unlike music, so artists naturally must learn art from teachers in schools. Also learning art in a class is a MUCH different experience than learning it on your own. It’s about the same as the difference between trying to teach yourself to play an instrument and learning from a maestro.
Famous musicians are taught by teachers all their lives – I don’t know of any famous musician who never had a music lesson. They have even MORE training than most artists do because it usually starts at a young age. In art, there isn’t the same tradition of one-on-one teaching, so the equivalent is to attend a good art school. Learning to write well is not as directly comparable, as it mostly comes from studying great authors (whether that be in a classroom or simply as one’s own reading material).
It is of course possible to teach oneself to be a good artist, if one has the dedication and the right learning materials. However, it is MUCH harder work without good teachers to give you regular feedback and the right techniques, and often self-taught artists don’t develop as far simply for this reason (I’m speaking from experience here. I learned ten times more in my three years at university than I did in the decade before it trying to teach myself). As such, famous self-taught artists are hard to find, and this is also the reason employers look for art qualifications – it’s not discrimination, it simply assures them that they are hiring someone who is well-trained and versatile and has learned from professionals, and not someone who learned to do the material in their portfolio well but will fall on their face if they are asked to do something else.
I have never experienced shunning of very talented self-taught artists – rather, they are admired, because of how hard they must have worked to get there. But they are hard to find in my experience.
Formal training in any discipline is a very good idea. A foundation in color theory, design, composition, technique and history are invaluable. If you can’t go to an art school there are many resources for teachers of all media on a small class scale or even private lessons. Community colleges and Art Guilds often have classes available. Self taught artists are all over, but I don’t think they are shunned, I graduated from art school and not once has any employer asked me for my “credentials”. Your portfolio and your experience speak volumes. Many artists are formally trained and not all that good, and many self taught artists are fabulous.
Self taught is a misnomer. No one is really self taught, if they are reading books, the author is their teacher.
Check out the artists on artid.com and you will see a whole spectrum of study for none to tons. Ask those artists what they think about the importance of training.