Imagine something like RSS feeds plus reader for Twitter. There is a screen to view the entire chronologic feed. In addition there is a feed for every followed user and one only consisting of retweets and quotes.
Like in a RSS reader tweets can be read, naturally this works across the different feeds without additional work on the user side. With continued usage and consumption the computer could make suggestions whom to unfollow to reduce the noise level.
Maybe the software also supports regular RSS feeds along the Twitter feeds. A single place to consume information. Something even better would be a feed consisting of linked content based on the tweets.
To me this sounds like a massive improvement to the current situation. I wish somebody would build it.