So I've this theory in my head for a long time now. Btw this might contain a spoiler or two if you haven't seen Flurry Of Emotions or S8's final. So be warned. Let us begin with this.
Cozy Glow's plan seems a bit unfinished to me. After all, her goal was to get rid of all magic yet did not do a thing regarding the Tree nor the Elements. And after she was caught, sealed inside Tartarus likely without her parents' knowledge mind you, and she just smiles. But...if her aim was to get into Tartarus why didn't she just do so and not alert anybody until it was too late?
My guess? There's something in there she wanted, but what could that be? At first my theory was the Alicorn Amulet which I believe is the 7Th Element, corrupted. But there just isn't anything to back it up---but I'll post what I do know:
Where was I? Ah, yeah my theory holds very little water to what others have said. But my next theory could very well be true. Is it a known fact within the show that if it's in a book, it's canon. Nightmare Moon's return (which is a paradox when you think of the sealed forever bit, me thinks Celestia lifted that seal herself), the Dazzlings, Tirek's first defeat, and even Snowfall Frost's story could had been true.
And Grogar was name dropped in Flurry Of Emotions. In a book, being defeated. And where do baddies go when their defeated and not stoned? TARTARUS! Cue Spike Whose Grogar? Here's his Wiki page.
So my theory is that Grogar is what Cozy is after. But then, why alert Equestria? Why bother with the first plan? I have an answer, and it's from a brony who I wish was still following the show.