Oooooooooh!What if instead of types, the E4 had their own strategies? Teams with high HP, or speed, attack, defence...
Different battle styles would be cool. Doubles, rotations, etc.
A strategically designed Elite 4 and Champion would be amazing to have. Now that would be a pretty fun Elite 4 to go up against, each with their own opinions and reasons as to why they specialize in the area of their choice. It could be annoying too, but a welcomed challenge nonetheless. I can see one of them mastering the art of Attack, the other Special Attack, another one could be Speed, and then there's the fourth member who can specialize in both Defense and Sp. Defense with HP included.
Meanwhile I could see the Champion having a well balanced, well put together and competitive team of high leveled Pokémon.
They could keep the specialized typing if they wanted to, but with an idea like this, I'd rather the Pokémon come at random so the different stat strategies can work out better.