They're different mechanisms.
Teaching modifies the learner. Prompting doesn't modify the model. It provides additional context that influences a single inference. A person who has learned something can apply it years later without being reminded. An LLM generally cannot unless the knowledge is incorporated into the model itself or provided again.
Right, but "provided again" is what SKILL.md or whatever else are for.
The value of LLMs is that they're stateless. With sufficiently detailed documentation and a well-bounded task, they are quite useful.