tGH was the closest she came, by trying to hide him, but that was a PoV trap issue. She did not know as we did, that they were important central characters in a fantasy series for whom exceptions could be made because a way would be found around the curse. She was actually doing the equivalent of hiding a demonically-possessed, ebola-infected, nuclear-bomb-strapped-to-his-chest level of menace to everyone she knew outside the Two Rivers from the people who would have saved him from madness. As Nynaeve had told him when she found out, "you are too dangerous." And she left the Two Rivers for purely altruistic reasons, not a craving for adventure, so she can be given the benefit of the doubt on any charge of cowardice. It's telling that Mat & Perrin only find out after it becomes clear that the Aes Sedai are not going to do anything, and Min & Elayne after it becomes clear that he's the Dragon Reborn. Because sane, normal or sensible people WOULD have done the right thing and turned him in, for his own good and that of their mutual acquaintances. Egwene is only nice to people in the following situations: when she can shaft someone else, when it benefits her or when it is absolutely the wrong thing to do.
In tFoH, she mostly carped, complained, interfered in his love-life, behaved so that the two companions who had known her the longest independently concluded she could not be trusted, and was so thoroughly willing to betray him that even Moiraine was forced into the role of defending his privacy. When he asked her for something important, it took her three days to agree to do her part to help her friends in a battle against unquestionably evil people, all over an obnoxious and selfish White Tower restriction. She had no problem betraying the Tower's rules for personal gain or convenience then, previously or later, by passing herself as a full sister, by revealing secret histories or by sneering at the Three Oaths when it comes to personal dangers.
In tDR, she was at the absolute nadir of her character, because she spent the entire book behaving hypocritically, to the extent that Elayne, who goes to absurd lengths for Egwene was actually driven to slap her. This is the woman who spent weeks or months in the same building as the man she loved, but never said a word or acted on her feelings because of an inactive prior claim of Egwene, despite her willingness to defy her mother, her nurse and her sense of propriety for that relationship - yet she would not speak so much as a word where Egwene had a right she gave no sign of exercising. The woman who is that deferential to Egwene was driven beyond all tolerances to slap her upside the head by her ongoing treatment of Nynaeve. And there is nothing in tDR that you can point to that is the least bit altruistic on her part. She took Mat to Tar Valon, but she was going there anyway. She went to protect Callandor, but she was going before she had any idea what that meant to him and did so because she was being given a command by an Aes Sedai under highly suspicious circumstances (close on the heels of a lecture and assigned punishment for having done that once already). She did NOTHING for Rand's benefit in that book.