Specifically, what I want is for the Tweet button to be able to create Tweets of this form:
In TweetDeck, Tweetbot, etc, the embedded picture auto-displays, significantly increasing the eye-catching power of that Tweet. For extra points, it would be doubly awesome if Twitter recognized the image as a thumbnail and clicking on it caused a click-through to the content URL instead of showing an expanded version of the thumbnail, perhaps also suppressing the URL display of the thumbnail in the Tweet text.
Alternately, you could make the Summary Card thumbnail auto-display, since it almost does what it should but it currently requires that extra click to Show Summary which makes it less valuable.