Unforunately in this released form there isn't too much of a reason to do so, outside of this one enemy presented has a shoe-horned weakness to left mode abilities but that isn't telegraphed or informed very clearly outside of one small line in the combat log.
The idea was originally formed around having to dyanmically shift between the two modes. When you reach the max intensity of one area you are forcibly returned to a neutral mind, and temporarily would have the one you just exploded out of be weakened, but the opposite mode would be boosted. Reaching either logic paradox or lucid daydream would also enable additional effects from certain abilities for their duration. An example would be By The Book not just protecting you from debuffs, but it would reflect them back at the enemy for a few turns increasing it's effectiveness.
I posted a couple images in a reply to another comment above that shows the actual diagram that was the basis of the build.
Thanks for the feedback!