The “higher” magical beings - fairies, witches and wizards, elves - have the greatest powers. The “lower” ones - the sprites - have significantly less and resent it. The fact they wouldn’t handle extra powers well they ignore.
Dwarves and trolls fall in the “mid-range” and, to be fair, everyone, including the sprites, has the chance to earn magical gifts from the Queen so even the lowliest sprite can add to what they were born with. The schools teach relevant skills to the relevant groups and each group specializes. There’s a reason why nobody other than a dwarf can mine and go into raptures about gold. Some things just are in the blood!
The Witch’s dragon wanted to experiment with genetics by turning Jenny into a lady dragon and mating with her, figuring their offspring would inherit her magical skills and making dragon kind independent of those like the Witch without whom he could not exist. He was right to think along those lines. Jenny was equally right to be horrified by the idea!
Fairies are the top beings in the realm, mainly because it is run by a Fairy Queen. Earth depictions of them as twee are despised. The only thing twee about Eileen is her collection of classic skirts made out of a certain well known material! The godmother class is the highest kind of fairy and it is from them recruits for the angels are usually found when godmothers reach the end of their time in the Fairy Kingdom.
Fairies like Hanastrew are not yet godmothers but are clearly going to get there. Those like the fairy squad will be the working fairies, some of whom will gain promotion, some of whom will stay put. Not every fairy wants to be a godmother - a great deal more responsibility comes with it. Fresdian (Rose) managed to disguise her true godmother class to avoid those responsibilities. All fairies practice their skills regularly. Most fight like demons too when called on to do so by the Kingdom.