This, this, this, this, exactly. It's part of why twitter is so much more enjoyable than facebook -- it's a simple, understandable stream of everything.
My experience is very similar to yours -- even with "most recent" (which is really "bias by recency a bit higher in the selection algorithm," as near as I can tell), I miss all sorts of things I really care about, (while still being bombarded with stuff I don't care about).
I am not, in general, a fan of machine-selection of relevant items. Even for a human to intelligently edit my fb feed would be a challenging job, and until machines begin to approach the intelligence of humans, they will do it poorly.