Everyone loves to claim that George signed off on her but dude was checked out at that point and in talks to sell, so he wasn't being as particular about new content because he was removing himself from it. You can't have part of Anakin's fall be that they won't grant him the title of Master and then turn around and make him a Master. You ascend from knighthood to Master-dom by taking and training a padawan, it has nothing to do with sitting on the council because that is a unique position that requires you be a Master but is distinctly separate from it. Only to have them turn around; a council who was distrustful of Anakin and thus refused to give him the Master implying they are refusing him the seniority, respect within the order, and right to train a padawan- and decide to assign him a padawan. Which is further against precedence because Knights are supposed to choose their padawan.
You don't have to be a Jedi Master to have a Padawan of your own. Kenobi was just recently promoted to knight when his tutelage of Anakin began, and he climbed the ranks from Jedi Knight, to Master, to Council Master. Also, the explanation for Yoda giving Anakin a Padawan was to teach him maturity by putting him in the same predicament his masters often find themselves in when they deal with him. It basically was a big fat "fuck you" to the boy, with the Council hoping that Anakin would mellow out once he sees things the way they see it, from a mentor's point of view.
Also, them denying him the Master seat was due to him not blindly obeying them and still having his own dark streak. Making him a master would grant him access to the Jedi holocron vault, which the Jedi obviously wouldn't want. Someone with that much darkness being given access to all the Jedi Order's secrets? That's something the Council would be very scared of.
There was also the fact that the Jedi Council were more than a bit vindictive on their own terms; Anakin was nothing but polite and mature up to that point, but the Jedi resented having Palpatine interfere in their affairs, and denying Anakin the Master rank was their way of flipping the bird in Palpatine's face. They couldn't openly shit on Palpatine without being accused as traitors, so they did the next best thing and took out their frustration on his patsy, telling him that "no, you can't make him a Master, only we can." For all the times the Jedi claim the moral high ground over the Sith, they cam be just as vindictive or murderous as the Sith; the only difference is that the Sith tale charge of their own destiny, while the Jedi enslave themselves to politicians who have no problems dumping them like used tampons.
Her popularity was manufactured with some of it being borrowed from her being reminiscent of Shaak Ti, who was a pre-established powerful female Jedi.
Not quite. Most people who salivate over Ahsoka don't even know who Shaak Ti is, which is a shame, considering that the latter had a somewhat important role during the Siege of Coruscant.
You also can't just input some new person into a storyline that would have colossal consequences on a pre-written story and never have them mentioned, it's poor writing and lazy. Some minor character mentioned or seen in passing, sure, they did that with Quinlan Vos; some background dude in TPM that got expanded into a whole ass popular character, had ties to Obi-wan, but whose presence and history changes nothing. Inserting a never heard of before Padawan to a dude whose the major player in the story and whose story has strong themes of abandonment, obsession, a need to protect to the point of destruction, etc. who is explicitly denied the ability to be a Master as part of that arc, it's nonsense. She might be more 'likeable' but she's threaded into places and tied to characters and given abilities that are strait out of this is my super special fanfiction OC.
The problem is, Lucas was scarred by the negative reception the Prequels got, so he tried to rehabilitate the PT with TCW, and since most PT haters don't know the general SWEU lore around the PT, he decided to give Dave the right to bulldoze any SWEU content that might get in the way since TCW is made to appeal to normies and PT haters, not lore aficionados and hardcore fans, and they won't notice. People who hated the PT like Doug Walker loved TCW, so it seems to have ths desired effect of making normies appreciate a period of SW that critics panned, but at the cost of the people who fell in love with the original Clone Wars lore which was rather airtight and didn't have space for a story where Anakin has his own padawan.