How much friction is there really in adding “toilet paper” to your shopping list and grabbing it during the next grocery run? It really feels like a solution in search of a problem.
Not much, but a little. You don't find yourself thinking, "I'm running out of shampoo, surely I will remember it for the five minutes it will take to finish my shower, then put it on my list." I fail at that all the time.
It's the firstest of first-world problems, and I sure as heck don't see putting a "shampoo" button in the shower. But it kinda doesn't surprise me that at least some people wanted them.
I suffer from depression as well, but I don’t think dash buttons would do nearly enough to help me (not being able to do basic tasks is a symptom, and no amount of automation will make the depression go away). And at least for me, getting out of the house helps. It forces me to shower and put on pants, otherwise I run out of toilet paper and detergent.