Cozy Glow even before she revealed her her true colors in school, showed pretty big red flags.
She caused the non-pony students to doubt whether they really improved or even had the ability to do so.
And when Smolder questioned why Cozy Glow was replacing Starlight, a perfectly reasonable question, Cozy simply states how they are not scheming dragons but ponies and Smolder needs to do extra friendship homework.
Cozy was creating an unequal and toxic school enviorment for the non-ponies. It doesn’t help she is also the teacher’s pet and therefore some unwritten authority and is also charismatic.
Honestly she should have been punished and disciplined just for these actions. At the very least be told not to demean the other students especially to her fellow ponies.