Die size increases are suposed to be a set thing in D&D. The most basic example would be the improved natural attack progression.
Supposed to be, but are not. Tables conflict when it comes to odd starting points and high end advancement. Which should be used?
Unless, of course, by 'die size' you literally mean d3->d4->d6->d8->d10->d12->d20->d100. That would, though, mean that a large Scholar at level 18 would be doing 1d100 damage with unarmed strikes. Which is quite unconventional, since standard size increases cap damage at multiple d12s.