Twitter would be really really cool if you could have your lists and then swipe through them like you do with the "Moments" feature (which is awful)
I actually use Facebook the same way too.
Yeah, I'd probably like this. I follow a LOT of people (right at the limit of how many you can follow) and I never expect to read every tweet. I just expect to check Twitter every now and then, and find a few useful / interesting nuggets of news. And occasionally I do a #hashtag search if I want to catch up on a specific topic.
So, for me, this kind of feature makes a lot of sense, as long as the algorithm does a good job of picking out the "good stuff".
It may not be for everybody, but I can see this being valuable for at least some percentage of Twitter users.