"Most Recent" does not by default display all the posts from all your friends either. Facebook has some algorithm for "determining" what posts you would most like to see. It's funny how it considers game and gift notifications or places' check-ins must-see news. So anything of actual interest gets lost in the trivia of who's having lunch where, and who sent somebody hearts or flowers.
Unfortunately, even if Facebook implemented a different ranking system to separate wheat from chaff, most people still wouldn't be satisfied because each of us have a different idea what is important. (One exception may be that no one likes to see game or app notifications.) Maybe you want to see someone's cookie recipes, but not their political rants. Check-ins into places are noise, unless it's someone whose whereabouts you temporarily (or permanently) want to know. Not necessarily a crush -- maybe it's a person at the same conference you're at, who knows all the best parties.
What does "show me more like this" mean?
One way to implement such a system would be to allow you to rank your friends posts by desirability. The ranking system could be similar to pandora.com: show/don't show me more posts like this. (Your thumbs up or thumbs down rating would not be seen by your friends, of course, to avoid unnecessary drama.) The question is, what exactly "like this" means? What criteria should Facebook infer from your like or dislike? If the rating system was anything like Pandora's the last time I listened to it (I gave up 2 years ago), it would be irrelevant, because "lead female vocal, acoustic piano, and minor key" does not begin to capture what I like in a song; it's more of a mix of elusive qualities relating to the progression of the chords.
So how should we tell Facebook what we are looking for in a post? Perhaps each user could have their own taxonomy of tags to apply to other people's Facebook posts. The taxonomy could use semantic web methods to enable powerful sentiment analysis (how you feel about a particular person, event or organization, such as this Evri API). After a user has tagged a sufficient number of posts, Facebook would have learned what is relevant to him or her, and would tag the posts before the user does, so as to filter out the posts the user doesn't want to see.