Instead of traditional schools, I would love to see a game where the "magic" is from the culture's heritage - an martial culture would focus more on focusing "magic" through martial arts - like spellsblade for example -
In today's world, when you look at different cultures and how "magic" was in their past, you'd see that different regions had very different views and usage of magic.
africa - voodoo(vodoun), thakathi, sangoma, inyanga were distinct from each other but still similiar
europe - wiccan/druidic/sorcery/wizard
Americas - native americans had a huge variety of unique "magical" folks that worked in different ways
asia - shinto was shamanistic to some extent, mambabarang/mamalarang in filipino (used beetles for their magic), suangi in new guinea (somewhat blood/soul cannibalism related magic), and quite a few others
All of those different ones would have different things that they claim are achievable, but do it in very different methods with various beliefs related that would make it so that they really couldn't learn many others due to belief conflicts.