This isn't a particularly high priority, but it would be nice to have the first paragraph of docs pages show up when searched or posted in Slack, Discord, Twitter, etc. This is done through the description meta tag, as well as Open Graph, etc. As the description meta tag covers most of the potential use cases, the others can wait.

What implementing this would entail is either manual addition of meta tags, or an automatic transform step that grabs the first paragraph of the relevant RST source. [1]

http://www.sphinx-doc.org/en/master/extdev/appapi.html#sphinx.application.Sphinx.add_transform