Mocha's gonna give a different perspective as someone who Redeemed Cozy in her own AU. I wholeheartedly believe at the time, Cozy should have been turned to stone, and here's why.
First of all, the "She's just a child" argument, doesn't fly. That would only apply if she didn't know full well what she was doing, or what her actions would result in. We are shown multiple times that Cozy is fully aware her intentions are evil, manipulative, and for her own gain. Even from her introduction, she is shown to fundamentally misunderstand what friendship is, even if she claimed she only did it to have the crusaders in the school with her. That in itself is trying to manipulate a situation to her own advantage. She needed friendship tutoring to begin with because she didn't understand it.
Second, she was PEN PALS, with LORD TIREK. Every pony knew what a danger he was, and she knew he had information on how to steal magic. What she initially planned to do was gut her world, to her detriment by the way (she wouldn't be able to use Pegasus magic) and when she was stopped, she was fully prepared to enact her plan elsewhere before the threw her in Tartarus, (which was their first attempt at dealing with her, as she had proven herself to be more dangerous than any villain before her next to Tirek)
Thirdly, When cozy was in the final battle, she attempted to KILL twilight with the other villains, and further, was GOING to help kill her friends after they succeeded in taking over. Cozy Glow had made herself a Harmony Level Threat. The only thing they could do to preserve piece, was turn her into stone. She may have been an accomplice, but accomplice's also go to prison if complicit in a crime.
Cozy never stopped to reconsider her actions, she did not accept the chance to be redeemed when offered, she did not WANT to be redeemed. We see her fear of being turned to stone, but that's not remorse, she's sad she got caught.
Do I think she was an irredeemable villain? Yes. Is she a child? yes. But does that absolve her of her knowingly evil actions? HELL BUCKING NO.
I think after some time in stone, she can be released and redeemed similar to discord. But at the time, that punishment was warranted and deserved. This is purely my opinion. 🍫