I have figured out how to balance champions.

Throughout history, itemization has been very difficult. We have had accidents where Yi, Tryndamere, and Tristana built deathcap. We have had Sorakas who didn't build support items. Lulu's who thought they were a mage. Alistars and Tarics who bought machetes. Furthermore, it was found that DFG, an item which is designed to increase a champion's single target burst, gave champions a lot of single target burst.

Despite RIOT playing whack-a-mole with issues as they come up, I think the conclusion is quite clear: items are hard to balance and promote unwanted diversity. Instead, the shop should consume your money and replace them with a pre-determined stat package which is unique for each champion.

The advantages of this technique are obvious; no longer will RIOT have to suffer through champions being diverse in a way that RIOT didn't intend to occur.