House of the Dragon Cut a Major Alicent & Daemon Book Storyline
And why did the showrunners decided to cut it? Because it would have ruined Alicent's arc in the show.
House of the Dragon is based on George R. R. Martin's book Fire & Blood, the most complete version of the prequel story, describing the events of the Targaryen civil war, the Dance of the Dragons, but a major – if only potential – Alicent and Daemon storyline was conveniently left out of the show.
And for a good reason.
The show's audience may be shocked to know what might have happened between the two characters, who opposed each other throughout the show, if we take certain parts of the book's narrative as true.
In the book, it is rumored by the court fool Mushroom that Daemon deflowered Alicent. The show's writers left this story as a rumor and merely hinted at a flirtation in the first episode when Daemon asks for Alicent's favor in the tourney as a way to upset her father, Otto Hightower.
The exclusion of this fling was the best decision given the direction in which the writers seem to be taking Alicent's character. If Daemon took Alicent's virginity, it would not only change who she is and her relationship with Rhaenyra, but turn their whole rivalry into effectively a love triangle.
And then again, Mushroom is not exactly a reliable narrator. He is one of three men from whose perspectives the book is told. All three are biased in their own ways, the readers are left to guess which version is the truth.
However, Mushroom is probably the least reliable of the trio. He is known to have a flare for drama, a penchant for exposing dirty laundry of the characters involved in the story – or, perhaps, inventing it wholesale – and a bias toward Rhaenyra and her party. In Mushroom's version of events, Daemon takes Alicent's virginity, which is why Otto, Hand of the King, hates Daemon.
As one of the showrunners, Ryan Condal said: "Sometimes they all get it wrong – sometimes Mushroom's even right, by chance."
In any case the showrunners and Martin decided to present a single factual timeline by taking elements from all three perspectives. Something therefore had to be cut, and Mushroom's accusations against Alicent ended up among the cut parts.
Speaking about bias, Mushroom also implied that Alicent slept with Old King Jaehaerys when he was sick and Viserys before Queen Aemma died! Now that's some hardcore vilification of your political unfavorite.