I am about to finish my first time through the series (listening to the excellent audiobooks). And I agree with OP that somewhere in the second or third book, R

I am about to finish my first time through the series (listening to the excellent audiobooks). And I agree with OP that somewhere in the second or third book, Rand annoyed with his slow character growth and refusal to accept that he was the Dragon. I think the second book is even my least favorite of the series. The early books are also somewhat repetitive in their structure: Rand goes on a quest and defeats a Forsaken at the end. However, the series starts to shift in a few ways not long after where the bulk of the books is about his allies on their quests scattered throughout the continent and they are far more interesting than Rand’s brooding. It also occurred to me in the last book or two that Rand’s slow growth may not be the most enjoyable to read but it is realistic — the story only spans two years or so and Rand has little time to actually process what is happening to him. He kind of acknowledges this in the last book, when Moraine remarks that the three boys she took out of the Two Rivers have grown up, and Rand says something to the effect: “no, only Perrin has, and when it comes to Matt and myself, I just hide it better.” There is also all the growth that you mention as well as his somewhat immature attempt to harden himself in preparation for The Last Battle and his final realization that strength does not come from suppressing all his emotions.