Facebook is doing this for a while. Pretty sure they always checked privately sent links. Some years ago I sent a .tk domain to a few friends and it got shadow banner after a few minutes (it was a harmless meme site).
Hackernews does shadowbanning as well.
It was done at the unnamed social network I worked at, over 10 years ago.
To combat spam, mostly. People posting links to scam sites to watch sports games.
When faced with software/malware that was appending links to user's instant messages back in 2005, back-end code to silently drop the user's messages was put in place. This was a messaging service that had ~200 million users.