I can't fathom why you think a sheet would have 30 action skills for magic types. There are seven magic types, they would be action skills. If it's not actually possible to make 'magical ability' a core attribute (and maybe it's not really all that desirable?) then using the core skills to as proxies makes perfect sense for all but physical magic, which is mathy and intelligence-based, because it's physics, not phys. ed.
I'm not talking huge lists of action skills, but rather, huge lists of background skills (which happens anyway) which are not rolled but which you need to buy to have a chance to roll without fucking up. This would make it hard as fuck to min-max, and also mean that after the game's been around for a while and you get inflated sheet dinos you can still easily write story that allows a Brakebills Freshman to do shit that the dinos cannot do, simply because she grew up speaking Cantonese at home and they haven't learned that one.
And be consistent with the source material, where doing magic demands that you have a very broad education.
The way it describes circumstances, yeah, everybody knows them after studying a while, but it translates to me not as 'unimportant colourful setting element to be ignored' but as 'No earthly circumstances are so difficult that characters who have Adjusting for Circumstances to 5 won't have an automatic success unless the GM says it's raining frogs or something' sort of deal.
Btw, I've got four cores, not six.