It could be a side effect of 'spaghetti code' issues with how blue mage's leveling works, rather than an active decision that "blue mage should not be allowed at do MSQ".

It can't just be about not wanting people to level that way, because it gets so much EXP from enemies compared to the slivers you get from quests.

Maybe the multiplier on battle EXP would apply to quests too?

Or does blue mage have a lower amount of EXP required per level to begin with?