IMHO it's best to be active and there while putting them to bed, and so you may as well read the story yourself. If you do it well, they'll ask questions, interact, and learn things, laugh, etc. I can't see this being replaced by technology any time soon, and I don't know why anyone would want it to be.
I don't think we ever positioned the site as a replacement for a parent or grandparent who is there. That said, my three year old requests stories to be read to her "on the computer" where we record them together and then she watches them back sitting on my lap.
Or maybe this is it, and you need to add something happier about it? It makes me think of my daughters' grandparents who are quite far away, which is a bit depressing. The positive side of things, of course, is that 20 years ago they would have only got brief phone calls, and now they can do stuff like this even if it's obviously not as good as being there. So maybe some kind of positive spin on it? Target it more at grandparents? Just thinking out loud...
Why not a standard PC built into a teddy-bear, simplified and locked down for just this application? Sell it as a $500 dedicated device to the business (wo)man who's away from their kids on a business trip.
[EDIT] p.s. - wouldn't the iPhone screen make the text too small for the child to read along with the parent? Is reading along an important part of the experience?
Put all your focus on marketing now.
I'm not saying iPhone wont work at all, I'm saying there's probably an additional opportunity (maybe better) for a bigger device, designed specifically for the task, and sold at a healthy margin (people who go on lots of business trips normally have above average income).
http://www.youtube.com/watch?v=-kwjYSn03-M
Original pitch: