Corlys and Rhaenys anon here. I would like for people to finally understand that the reason why Rhaenyra will never be explicitly reffered to as "beloved" in terms of personal relationships, especially as a wife, has nothing to do with her or Daemon in their intimate life, and everything to do with what she represents in a mysoginistic and patriarchal society: she is a woman that wants to rule, that effectively does not live by the rules imposed on her - not in her attitude, not in her personality, not in her position as heir etc.
Historically, women in positions similar or identical to Rhaenyra are constantly attacked, especially in historical documents. They are considered - by men generally, but by other women too - unnatural, anomalies that look to disturb the "proper" order of things. And these attacks do not resume only at them as persons - since they are unnatural in wanting to rule, they are also seen as unnatural mothers, wives etc. Every aspect of their personal life is under scrutiny and under attack as well. Sometimes they are not even considered women.
(See how The Shepherd reffers to Rhaenyra: “this unnatural queen who sits bleeding on the Iron Throne, her whore’s lips glistening and red with the blood of her sweet sister.”)
That's why we don't have romantic songs about Rhaenyra in the way we have about Laena or Nettles. Because Laena and Nettles do not disrupt the order of things in any way - Laena is won at a duel and handled between Corlys and Daemon; Nettles comes from nowhere and goes nowhere. They depend on Daemon alone to provide some importance for them. They are, in many ways, ideal for a patriarchal society.
Rhaenyra is not only proactive in deciding to live her life as she desires, but she is also held guilty for a war that was never started by her, called a whore repeatedly, dehumanized to the point of disbelief. But it's not hard at all to discern, from the objective actions of the people in her life, how beloved she was not only by Viserys, Daemon and all of her children, but by the people also.
I'm sorry this turned out so long, it's just... I wish people would comprehend this and stop painting her as unloved, mocking her, calling her names. Because in doing so they fall directly into the trap of the maesters who obviously hated her.
The simple fact that people continued to fight for her even after she died, that it is her line that continues, should tell people who was in the right. Alas, this fandom was never known for critical thinking.