Adding work into the shower would diminish it's idea generating powers.
The reason we are able to come up with good ideas in the shower is that our mind isn't otherwise occupied by doing anything else. We aren't on our phones, watching TV, having a conversation, or working. Our mind has no obligations and the act of cleaning yourself doesn't require much mental load. So our mind is free to drift and think freely about whatever it wants. We don't have many similar times of distraction-free brain freedom in our modern lives.
Add in a task like taking a meeting, and now you've removed that key no thoughts head empty feature of showers that leads to the brain blast.
We have plenty of distraction free brain freedom. It's the formality of the meeting. If I'm fighting to see Karen through the steam and pausing to spit toothpaste I'm less concerned about the passive aggressive way she's telling me I didn't submit my code on time.
Of course. Plus shampoo, toothpaste, razors and body wash would be claimable on tax. Haven't figured out how to improve the shower coffee situation though.
You know, if all meetings were only held by people on the toilet, we could avoid all of those unfortunate embarrassing incidents when that one person forgets to mute.