To me, the most interesting element you point out is the notion of textshots-as-lead-gen. And I’m not even sure we fully disagree here, but I think it’s an interesting, nuanced issue (to which there probably isn’t great data either way right now).
I could see that for a lot of articles, a textshot could basically be a “tl;dr” version of the post for some people and so they don’t feel the need to click through to the actual post. Or, it could “spoil” the main crux of the article (in either a good or bad way —hello, @SavedYouAClick). But I would argue that most of the readers who no longer feel compelled to click on said article after seeing the textshot are the ones who would quickly churn out anyway.
That is, they would click to see what the article was, maybe skim it, then quickly close the article. They’re hardly valuable readers (though, undoubtedly, most publications would be happy to count them anyway!).
Ideally, the person creating the textshot is able to pull the most interesting/provocative excerpt of a post to share and it compels even more people to click through to the article to read it. Again, I have very little real data, but the ancillary data in my own usage suggests this may be the case (i.e. Twitter’s analytics tool shows you not only favs and retweets but link clicks).
In a way, I think these textshots are really just the extension of a link blog, but on Twitter. The best such blogs tend to share something more than just the link. Sometimes it’s their own commentary on the issue, but often it’s also an interesting excerpt from the article being linked to. Just like a textshot.
I agree though that it’s not great that there are so many different varietals of these textshots and the way Twitter currently presents them is far from ideal. Which isn’t surprising since this is, of course, a hack.