Something interesting to me that I think fails to be taken into account of the criticism "the Dragon Reborn can be more than one person or any gender" plotline in the show is that I feel most of the critics seem to mistakenly assume that the show is presenting it as a fact that the Prophecies of the Dragon are flawed, and that the show is presenting Moiraine's personal ideas of the Dragon as ironclad fact.
When, in fact, if you watch Episode 6 closely, what you're actually getting is an argument between two diametrically opposed points of view a) Moiraine, who thinks the Tower prophecies might be innacurate, and who therefore thinks they need to cast a wider net for who the Dragon Reborn is and b) Siuan, who thinks the Tower's prophecies are accurate, and who therefore thinks that they should be narrowing the candidates down according to who prophecy says the Dragon Reborn should be.
So you've got a) Moiraine, who's travelled all through the Westlands, and heard a hundred stories about the Dragon from a hundred different villages, taking the argument that the prophecies of the White Tower can be fallible and that some other prophecy out there might be the one they're looking for. It's natural for her to take this argument, because twenty years of being outside of the Tower and hearing differing stories is naturally going to shape her mind to be skeptical that the Tower is the only authority in this, or that the Tower holds the only right set of prophecies. It makes total sense for Moiraine to put forward this argument.
And then you've got b) Siuan, who's stayed in the Tower, who leads the Tower, who knows first hand the rigorous fact and information storage protocols of the Tower, taking the argument that the Tower's set of the Prophecies of the Dragon are accurate, and that they should stick to identifying the Dragon Reborn using them. It's natural for Siuan to take this argument, because the White Tower is pretty much the only institution to make it out of the chaotic post-Breaking period intact, and from the start the Aes Sedai have shown a vested interest in ACCURATELY preserving information, to the point where the Tar Valon library has a copy of every single book in existence. It makes total sense for Siuan to put forward this argument that the Tower's prophecies will be accurate in a way that no word-of-mouth prophecies passed down through generations in some out-of-the-way village would be.
But, at the end of the day, that's just what they are: arguments. The show presents both Moiraine and Siuan's arguments neutrally, and with equal weight: it doesn't actually take a side. It doesn't actually say that Moiraine is right. It doesn't actually say Siuan is right. Instead, it lets them present opposing arguments for tracking down the identify of the Dragon Reborn, and then the plot moves right along without establishing either one as right just yet.
And the kicker is, by the end of the series, THEY'RE BOTH GONNA BE RIGHT.
Siuan is going to be right, because yes the Tower's prophecies ARE going to turn out to be the most accurate of the prophecies in all the Westlands that Moiraine has travelled to. ALL the Tower prophecies are going to come true, even if the Aes Sedai haven't interpreted them correctly.
And Moiraine is going to be right because there ARE going to be other people with accurate prophecies that will come to light: the Aiel and the Sea Folk. The Sea Folk prophecies of the Coramoor and the Aiel prophecies of the Car'a'carn are going to come to light, and they're going to be just as right as the prophecies of the Tower.
It's just… as a book-first fan myself who watched the show later, I have no idea how we book fans can be mad about this one, and I simply don't understand the criticism that this was a short-lived plot point with little value going forward. The show can only have created this argument if the show-runner has full knowledge of how the book series wraps up, a long-running thread that can only be proven in multiple seasons, rather than just a one-season mystery box. And they've even taken care to set up the opposing ends of the argument be Moiraine and Siuan, the two people who first started the quest together, the two people who first head Gitara's prophecy of the Dragon being reborn. In Season 1, they've set up an almost metaphysical argument between Moiraine and Siuan that can only truly be answered in Season 8 after the Last Battle, at the end of the age of prophecies.
Additionally, they're also foreshadowing an argument that's going to happen between Rand and Tuon near the very end of the series: what do you do when two sets of supposedly infallible prophecies seem to clash, as the Westlands and Seanchan prophecies seem to clash, re: the Dragon kneeling to the Crystal Throne?
What part about this shows a lack of forethought, of not thinking through implications? To me, it shows the opposite. It shows that they're thinking through implications so deeply that they've set up this overarching near-metaphysical argument in Season 1 that can only be truly resolved in the final season of the final episode of the show.