Personal Opinion: Board Size Increase would weaken OP characters without needing a nerf.
Right now, three of the strongest characters are Aurelion Sol, Draven and Vayne. Vayne/Draven can easily become hyper carries with a few items while Aurelion can blast a whole metric ton of units with his breath ultimate.
However, if the board size is increased, these units become worse. For one, corner camping is harder because units can't attack from ranged as easily and are forced to step up, freeing a backline for assassins to dive into. Second, the increased size mean that there is more room to maneuver. Aurelion's shout taking up 1-2 rows now is a lot more manageable when your units can be MUCH more spread out. Most of all, this still allows for both players to play wise with positioning and plan out their fights better.
Board size can be a tool for us to weaken strong characters without having to tweak their specific numbers.