Why do people get good ideas while thinking in the shower? I think several factors are involved. The first is comfort. You never hear anyone say, "I had a great idea while I was in the shower this morning, and it was when there wasn't enough hot water and I was shivering, and I was running out of soap and there was a knock at the door." Instead, the positive effects of the shower tend to happen when one is warm and comfortable.
The second factor is privacy. In the shower, your thoughts are unlikely to be interrupted. If the phone rings, you have an excuse for not answering it.
The final factor is the sensory isolation of the shower. The sound of the running water creates a type of white noise that drowns out distracting background noises. The visual environment of the shower is also bland and neutral. I would guess that people with those "shower radios" who listen to the news while showering are not inspired by as many ideas there. I have not seen showers with built-in TV or computer screens yet, but it is probably only a matter of time. Once those are common, the phenomenon of coming up with good ideas in the shower will probably disappear.