There must be a good way to find interesting original stuff on the web and present it to people who are interested without them needing to actively search for it or "follow" a bunch of people to maybe find one or two good pieces in between a pile of crap.

There are a few, but most of them are relying on passively gathered information and are limited to content within their entity.

For example, Spotify is learning fast, but their folksonomy engine is still ages behind has a tag based recommendation engine, which excludes gathered information, but is limited to posts.

What you're mentioning is what superfeedr could be used for; the big question is: how to you make this user friendly?

The gathered information (based on what was consumed) is easy for the user, but it's also highly unreliable, constantly restraining the interest circle of one.

When the user needs to provide the information, most of them will simply not bother.

Netflix is trying hard to do both: a minimal initial information provided by the user and gathering based on consumption; I'm not yet convinced, but this looks like a good alternative.

I think the technology is already there, but it's hard to monetize and therefore not receiving attention.

This is indeed a problem; monetizing this in my opinion is only possible with subscription to a service.