This thought came to me, of course, in the shower. I was happily showering, with the lights off as usual (because that improves the state of creativity even more), and the question popped into my head.
It is well known that thoughts and ideas come easier into the mind in the shower or bath. It wouldn't surprise me if important inventions have been first thought of there. There is even a subreddit dedicated to shower thoughts. Browsing through it is entertaining, but it doesn't solve the question.
I have a theory that it is related to sensory deprivation. Basically, when the brain stops receiving clear signals from one sense, it compensates by cranking up the signal from other senses. This is why blind people often have unusually good hearing, for example.
When there aren't any clear signals from *any* sense, for example in a sensory deprivation tank or simply half asleep in bed, the "background noise" of the mind gets cranked up. This is why we can hallucinate coloured blobs and static noise while we lie down in a dark room. A shower blocks the senses of hearing and touch effectively, by overloading them with noise signals. Turn the light off, and the sense of vision gets deprived too.
Some people have said that they have experienced actual hallucinations while showering with the light off. I haven't experienced that yet, but I certainly get more creative. Not only weird questions pop into my head, ideas for art and music frequently do.