@Mildgyth
Twilight tried turning ‘Friendship’ into an establishment, which was a flawed idea from the getgo. Most of the successes the Friendship School had were by coincidence or proximity, not by actual course design. The effectiveness of a friendship school is overstated.
There will always be those who feel at home rejecting the establishment, but that would not stop someone actually wise to make her see that friendship can actually be a meaningful part of life in her personally. It’s the very basis of the importance of individual attention.
This leads partially back to the issue that Cozy has no real backstory. There’s nothing to her beyond being evil.
Kids have no filter, so if an intelligent but young kid fully obsesses with the idea of being evil is the greatest thing ever, she would be terrible, especially in a world where magic exists.
But she is STILL a child. She is not the smarest person in the world, she is not the wisest person in Equestria, no matter how much evil she’s accumulated in herself, she still only has child’s amount of life experience to back it up. She has a horrible soul, but one untested and unguarded by years of experience. Saying she was a lost cause is premature.