The problem is simpler: the cost of disintermediating their service, e.g. to go ahead and build your own feed, is just too high. And maintenance is just a pain. It is far better to view tweets other's tell you to, than use your own feed.
What Twitter needs is better intermediation - they need better tools to tune in and tune out of streams. The need, for want of a better analogy, a way to change the channel from Election heavy tweets to NBA tweets, when your team is on and you stop watching the debates.
TL;DR Twitter makes it too hard to bother, most of the great tweet content is made available at some point, and you rarely regret missing anything.
Precisely. One strategy for addressing this in the near term is to create more tools and products for partners/distributors like Yahoo and HuffPo to find and present interesting tweets for their audiences. Twitter can't curate everything in house in the near term. Algorithms aren't reliable enough, so they need a mix of algorithms and people. Some of those people can be in-house, but the faster, more scalable way to reach every nook and cranny of the world is to outsource a bunch of the curation through distributors who understand different audiences. Users have proven they won't curate on their own. As a bonus, Twitter can analyze these curation strategies to refine its own machine-learning algorithms.
What Twitter needs is better intermediation - they need better tools to tune in and tune out of streams. The need, for want of a better analogy, a way to change the channel from Election heavy tweets to NBA tweets, when your team is on and you stop watching the debates.
TL;DR Twitter makes it too hard to bother, most of the great tweet content is made available at some point, and you rarely regret missing anything.