This is almost not constructive. 🙂
On the other other hand, I understand the problem: The use case is not very clear. The original ticket doesn’t say much about the reasons besides see Tumblr.
The main problem is the hybrid nature of post formats:
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They are meta data. Data handling belongs to core and plugins, not to themes. But they are used by themes only. So after switching to a theme that supports a different set of post formats all your former assignments are useless.
This results in a lock-in effect, something we avoid in themes usually: shortcodes, custom taxonomies or post types should never be part of a theme. -
They are a taxonomy, but the interface in the post editor treats them as mutually exclusive like a post meta field. This is not how taxonomies work in general, and it makes the choice unnecessary hard: an audio post can be a quote too, a link might be decorated with an image … and what about video chats?
I cannot provide real world examples. My clients don’t use this feature. I tried to offer it in some themes, but they ignored it completely, and no one ever asked for it.
I think the idea was to stop theme developers from misusing categories for pure styling and to get at least some compatibility between themes. As far as I can judge it, it didn’t work.
But I think it is worth being mentioned in a guide, especially explain how the choice determines the style more than the content (again: video chats). Justin Tadlock has written some posts about that, starting here.
But in development and documentation do not waste too much time with it. There are other, more important aspects of themes.