Eh, maybe you're right that card access is incredibly important. If so, the fact that the Mage Wars card pool is still fairly small might have something to do with why core set only books can still be viable.
I don't think they are. If viable means a reasonable competitive book, or a good causal one, then sure. But no Acid Ball, Disperse, Crumble, Disarm, Leather Chausses, Lesser Teleport or Rust? Each of those is a pretty big hit against 80-90% of books, without considering anything mage or book specific.
A lot of books easily run 6-8 Armour and Vet Belts, and you need Corrode to deal with that. 5.5 of the choices are about mana/effect efficiency and if you are paying an extra couple of mana every round or two, then that's enough to take you out of viable.
It's also possible that card access plateaus too. Maybe there are only a few expansions that a Mage needs to be viable in a competitive format at the minimum, and anything beyond that isn't strictly necessary from a competitive standpoint?
Definitely not all mages need access to all sets. In fact I've often opined to new players that you can actually get in striking distance of an optimal book with a core set, the mage's 'home' set (if not core) and one expansion. The Academy Base Set (ABS) really needs adding onto that though, more than the extra expansion in most cases...
Beastmaster, Jokhtari - Core, ABS, CoK/DvN?
Beastmaster, Straywood - Core, ABS, CoK/DvN?
Druid - Core, ABS, DvN
Forcemaster - Core, ABS, FvW
Necromancer - Core, ABS, DvN
Paladin - Core, ABS, PvS
Priest - Core, ABS, PvS
Priestess - Core, ABS, PvS
Siren - Core, ABS, PvS
Warlock, Adramelech - Core, ABS, FiF
Warlock, Arraxian - Core, ABS, FiF
Warlord, Anvil Throne - Core, ABS, FiF,
Warlord, BloodwaveCore, Core, FvW, FiF
Wizard - Core, ABS, CoK/DvN?
CoK is a good set for everyone, but not unmissable for anyone.
That list makes everyone pretty good on a Core and 2 expansions. The key things you are missing are Acid Balls and to a lesser extent Disarms almost everywhere, and Guardian Angel from all Holy books and a few others.
I wouldn't call them tournament viable, but more than casual viable...