Idea for a Cozy Glow backstory that wouldn't tie into the café scene a few pages ago:
At her old school, Cozy had bonded with a teacher named Mr. Kingside. Kingside was in charge of running the school's chess club, which met during lunch break and after school. Nobody ever came to pick Cozy up, so Cozy would be the last one to leave, and Kingside would often walk her home. Cozy was a bit of a problem child, one who would see what she could get away with. She was regularly talked about in the teacher's lounge, but Kingside never had anything bad to say about her.
Kingside taught her everything she knows about chess, and she quickly rose to the top of the chess club, where she remained for most of the year. In fact, she got her cutie mark the day she finally beat him. He was going easy on her, but not by much, and no one else in the club had even come close. There was something about his class and his club; he really was that one teacher who makes all the difference. Indeed, by the end of the year, Cozy was way more social, and the number of "Cozy Incidents" was down significantly.
And then tragedy struck. Due to a massive budget cut by the EEA, Kingside was laid off. Budget cuts were needed to pay for the construction of new schools in the far away city of Canterlot. They had been destroyed during the changeling invasion. Her favourite teacher was gone, the chess club was shut down, and Cozy was never quite the same after that.
In chess, there's a concept called "simplifying". Once you've got the board in a certain state, you start intentionally reducing the number of pieces both players have, which means there's less to keep track of, and makes it easier to win. I think an interesting way to interpret Cozy's plan is to look at it as "simplifying Equestria". Notice how her plan is all about getting key pieces out of the way. She wanted to create a simpler world; one where she's in control, and unforeseen things don't take things away from her.