The challenge for a medieval king, whether Henry I or the fictional Viserys, was to persuade the nobles to overcome their prejudices and not just accept but actively support a woman's ascension to power.
Henry I pursued measures to make his daughter palatable to them. Matilda, who had married the Holy Roman Emperor Henry V in 1114, returned to England a widow in 1125. Henry I, determined to forge a sacramental bond between his daughter and England's magnates, compelled his barons in 1127 to swear their support for her as his successor. Henry I then turned to arranging a marriage for Matilda so she could give birth to a grandson and buttress her position.
After Matilda's nuptials with Geoffrey, count of Anjou, the barons were summoned to renew their oath to her in 1131. A son, Henry, was born two years later, and a third pledge followed. Henry I died two years later of food poisoning after eating eels, a favorite dish of his.
The durability of his arrangements for Matilda's rise to authority was immediately tested.
Viserys in "House of the Dragon" works from a similar playbook. The worthies of Westeros vow their loyalty to Rhaenyra as royal successor. Once Rhaenyra becomes marriageable, Viserys fields a plethora of suitors for her hand. A reluctant bride, Rhaenyra finally accedes to a union in which she would "dutifully" produce a male heir but then let her heart have what it wanted.
The unfortunate result is her inability to conceive with her husband while having three sons by a lover. Her situation is further complicated by Viserys' remarriage to the lady Alicent, who gives him sons. Dangers stalk Rhaenyra's path to power. In Westeros, as in England, a princess is expected to guard her chastity closely until marriage and, once wed, to be monogamous and not to "sully" herself in order to ensure the legitimacy of her children — a blatant double standard when noblemen frequently had children out of wedlock.
Yet even rumors of female infidelity could threaten succession. Lineage matters. Blood binds, as evident in the streams of it running from family crest to family crest in the series' opening credits.