They actually did start to integrate them. Google Reader had native sharing functionality for several years. Then in 2011 they suddenly removed it and replaced[1] it with sharing through Google+. My small network of Reader-using friends were split over wanting to join Google+, so that mostly killed our practice of regularly sharing links with each other.
[1]: https://googlereader.blogspot.com/2011/10/new-in-reader-fres...