An American switching from an ominverous to a plant based diet saves approximately 219,000 gallons of water per year. The majority of this water is used to water crops that feed livestock. What could you do with that much water?
A typical showerhead uses about 5 gallons of water per minute. Low-flow showerheads hit about 2 gallons per minute, but let's stick with the more indulgent 5 gal/min for now. 219,000 gallons of water would allow you to shower for 1 month straight. When you finally emerge, wrinkly as a prune, imagine how much high quality, guilt-free thinking you will have done.
The human brain is increible at making comparisons and associations. Externalization of facts allows the brain to do this work efficiently without getting slowed down by things it handles poorly, such as memorization. In the shower, you have few distractions, novel sensory input, and your brain is free to do what it does best: explore and associate.
Once exiting the shower, thoughts are quickly lost. One needs a way to quickly and easily record showerthoughts before they get lost. Just as importantly, one needs to return to the thoughts at a later time when they can be acted upon. Thinking works well in the shower. Writing, not so much (although dictation to a recording device could work!)