Which is precisely why Richard Sutton doesn't think LLMs will evolve to AGI[0]. LLMs are based on mimicry, not experience, so it's more likely (according to Sutton) that AGI will be based on some form of RL (reinforcement learning) and not neural networks (LLMs).
More specifically, LLMs don't have goals and consequences of actions, which is the foundation for intelligence. So, to your point, the idea of a "skill" is more akin to a reference manual, than it is a skill building exercise that can be applied to developing an instrument, task, solution, etc.