Despite the disadvantages, I would really like an e-ink phone (and netbook) for the significant increase in battery life it could give. The software could be designed so that it is usable on e-ink. No animations, no reliance on color for indicators, flipping instead of scrolling, etc. As you say, it would only really work for static content, but for me that is fine.
Almost any phone not a smartphone could fit your description. There are so many phones that can last for almost a week, but all you can do is talk and text with some light apps.