A lot of excellent composers were essentially self-taught, Poulenc, Schoenberg, and Takemitsu among them. Bernstein was highly schooled in piano, conducting, and orchestration, but apart from receiving personal critiques from Copland (“This passage isn't you”), he evolved as a composer without interference. In fact, he mainly used his counterpoint classes with Arthur Tillman Merritt at Harvard as a stimulus to write his own spiky, dissonant, and rather Coplandesque piano pieces.
On one occasion, when Merritt pointed out that what Bernstein was playing did not fulfill the assignment, he pounded his fist on the piano and said, “Well, I like it!”
As someone who has now tried to “teach” composition for roughly fifty years, I would say that composers need information and practice most of all: information, practice, and support. Much of the information they need comes from hearing what they write. No teacher can tell them more than their own ears can. And if their ears learn nothing from hearing their own work, then no teacher can help them. But aside from information and practice and support, composers mainly need respect (including respectful listening on the part of the teacher) and to be left alone.
Erudition in music is a good thing, but music itself is not academic. It is actual.
Study that is beneficial tends to be at an angle to original work: playing, listening, score study, analysis of other (mainly older) music, ear training, counterpoint and harmony study, and many other kinds of practice and immersion in the substance of the art. Listening as broadly as possible is a good idea. You never know where the tentacles of a mind will stick: it could be in the Middle Ages, or in Indonesia, or in the West Indies, or Appalachia.