There are clients that kind of did, but one of the cool things about Google Reader that a lot of people miss is the social feed. You could share articles you found interesting and your shares would show up on the feeds of anyone who followed you as just another RSS source. It's just an extra folder of articles from your GChat friends that you can read at your leisure.
And it's people selecting articles from their normal reading rotation, so it was refreshingly clear of clickbait. People usually shared stuff because they thought their friends would find it interesting rather than distributing content designed to "go viral."
Once the ecosystem fragmented nobody has the critical mass to replicate the social features. It was nicer than what Twitter or Facebook do because it wasn't in your face.