Then it would still up to you as a "subscriber" to decide what of the things you're allowed to see you do want to see on a regular basis; it would generally be up to the user how lazy they want to be, and how much lazyness they want to tolerate in their inbox. Don't tell me it's hard before it was even tried?
Even a generic WordPress blog is better than Facebook in this regard, since posts tagged and sorted by tag.
By now, the average facebook user has accumulated so much "stuff" that it's hard to find certain memories...for example, you remember the caption of a photo (e.g. "kiss + in front of Times Square") but you can't find the photo because you have 20+ albums (which are incredibly hard to navigate). Search would help greatly here. And having filters to just look at all the times that you posted a relationship status, talked about a popular TV show, etc. would be great.
I don't know where FB could go next with this, though. Allowing that kind of search across all your Facebook network would be like the original News Feed controversy (years ago), times 10. I noticed that years after it launched, the feature to see the history between you and a friend is still buried. It's quite useful, but if it were more prominent, people would see it as very stalkerish (i.e. people checking on their significant others' interactions with friends they suspect of being possible cheaters)
Granted, 95 percent (or more) of Google's profit comes from search, so they're not exactly exemplar of diversification. But they do have a range of products, some of which are beginning to generate solid revenue (Google Apps comes to mind).
Now i got into habit of using chrome in private mode to actually Google for information.
Google is great for indexing and search global information database, Facebook is great for social connectivity and sharing.
No need to breed cat and dog into universal pet or judge that cat just become a better pet.
I wonder if Larry,Eric or Sergey have thrown any chairs though a window :-)