Just a word of caution: running iOS devices on constant power can bloat and expand their batteries. I don't think I would trust them to permanently run somewhere. Not sure if it actually is a fire-hazard but it sure ends up looking like it. Have seen this happen on iPhones and iPods that were used for automated testing and that were connected via USB 24/7.
Searching for "iPhone bloated battery" on any image search shows what it's like.