I don't think this is a bug.
Google (or Bing) doesn't find your post when I use the words from the image description. If I use the word tiananmen your question is my first result.
So even Google considers alt text not as content that is important enough to be indexed. Given the fact that the Stack Exchange Search engine doesn't even try to be better as Google explains why your post doesn't turns up in search results.
If the image description is that important you could consider adding it to the body post, if needed decorated with markup
<sup> to make the text smaller or maybe even a spoiler.
For your first two points, I don't see what you would expect instead? Does the image need to be included? Does the text of image description need to be included? The last one would give a lot of noise given the fact that 99 out of 100 the image description is the standard boiler plate text.
Those are more feature requests that have some negative sides that needs to be addressed carefully if proposed.
text that is very small to carry some info that doesn't attract attention at first
text not visibly only on hover