@Duke_Anax
Except that the grind DOES increase strength. They actually said that its one of the main reasons that Merlin and Shin's magic was so strong at base. The other part of Shin's strength is his 'image'.
They even gave a perfect example of how the grind increases strength by showing them the barrier. The same 'amount' of magic had incredibly dramatic differences when they used the artifact that utilized Shin's focus.
Its gas vs liquid vs solid, I think. Gas is what all the mages have pre-training. Then training makes it thicken or purify (the novel doesn't describe it well, lol). In short, the training makes 1 drop of mana do far more work. You don't get more, you just get a far more efficient fuel.
As for magic vs physical endurance, I think you're forgetting just how much of a physical boost Shin was using in a 10 year old body. They made it sound like a multiplier.