There isn't really much intuition to begin with, and I don't really think building intuition will be useful, anyway. Even when looking at something as barebones as perceptrons, it's hard to really see "why" they work. Heck, even implementing a Markov chain from scratch (which can be done in an afternoon with no prior knowledge) can feel magical when it starts outputting semi-legible sentences.
It's like trying to build intuition when it comes to technical results like the Banach-Tarski paradox or Löb's theorem. Imo, understanding the math (which in the case of LLMs is actually quite simple) is orders of magnitude more valuable than "building intuition," whatever that might mean.