Then there is keeping things to remember later. I do this quite often now for posts. Yes, I could copy & paste the text into a note-taking app, but why not just screenshot the passage? It's so much easier to do.
The same is true with sharing things. Aside from the aforementioned textshots, I often take screenshots of Tweets/Facebooks/Instagrams/etc, and share those with others on chat apps. Again, this is actually more seamless than copying and pasting a link. It also saves time on both ends as the receiver only has to load my image, not an actual website. (Facebook may be on to something.)
It's interesting to observe how taking screenshots has evolved culturally from a tool to capture app icons or Home screens into a way to share information quickly (despite its accessibility concerns) because most web services/messaging apps make it easy to preview images. Taking screenshots is also the most popular way to save controversial tweets or Facebook posts that eventually get deleted or edited.
The only time when I don't share screenshots of Twitter conversations or web articles is when I'm using Slack, which automatically pulls in tweets and headlines when you paste links into a thread. I guess this also says a lot about eschewing slow web views in favor of nimble inline previews.