BuddyPress.org

We do not show the preview of the URL in the actual activity stream. It shows up in the activity embed when you want to share your activity update on other sites.

Check out the codex article for more info:
https://codex.buddypress.org/activity-embeds

Your suggestion is something I’ve been thinking about as well, but this will be changing the default behavior of oEmbed items since BP v1.5. We might think about this for a later version of BuddyPress.