George used her as a plot device, the "Meereenese Knot," so to speak. She is a highly important character, but she had to be moved from the periphery without physically moving. Favorites? She calls Drogon her largest and strongest, but never her favorite. Drogon isn't chained up because he escapes. If anything, she connects to Drogon more than the others because she is his rider, and she cannot mount either of her other children. What has Stannis done? Lost every battle he's fought in the War of Five Kings (minus the Wildlings), gives up, and sails to the end of the world to "defend his kingdom." He's in the middle of a damn blizzard while the Boltons prepare to meet him in the field. Stannis is honorable, but what does honor get you? A false title and a seat where he can freeze his balls off at the Wall. Daenerys remembers her identity, her cause, her endgame all in one really hot adventure into the Dothraki Sea. She realizes she cares about her people at the end of ADwD, but she pities them rather than loves them. Her entire arc in ADwD was built around identity, and the loss of such. Daenerys thought herself a Mhysa, a mother, but she is mother to three and not thousands.
If you read the Arianne chapter from Winds of Winter, you saw that Westeros is frightened by the thought of dragons, let alone the last legitimate Targaryen. What do the lords of Westeros say about Stannis? They praise his victories from twenty years ago and then laugh about his blunders as "king." Daenerys has taken three large cities without the help of her dragons in a few months, yet Stannis has claimed to be the true king for nearly three years now. The only [wo]man I mean to bend my knee to is sitting in the Dothraki Sea, having miscarriages and riding dragons. It was the stags we married, and the stags are all but gone. KHALEESI OF WESTEROS. KHALEESI OF WESTEROS.