I've used countless 'read it later' services like Pocket, Instapaper etc over the years (even some on PalmOS...), but for me at least the combination of Twitter plus the much more reliable cellular data we have now has made them less appealing.
Twitter has advantages beyond just the links being shared - the tweets themselves are often interesting to me, and the list of people I follow has been carefully built over time to the point it would be annoying for me to switch again now.
I'm sure these are great options for others though, but I don't think I'm alone in using Twitter as a kind of curated RSS replacement.
Maybe 7 years ago I built a service that would track links from your Twitter feed, mainly because I was posting links I found interesting and wanted a way to refer back to them later.
I intended to have it track all links from people you follow too, to give a curated list of links, but Twitter was aggressively making changes to restrict their API so this became impossible.