I think you're misunderstanding something here. "Chat Control" is a term invented and popularized by privacy groups who oppose any scanning of private chats for any purpose; any confusion caused by having the same term refer to different things has to be laid at their feet, although they argue it's appropriate because any kind of scanning is abusable in basically the same ways. The people who support scanning private chats don't use the term "Chat Control".
And the underhanded way of trying to get something as controversial as this to pass, says a lot about the politicians pushing this agenda.
Chat Control is about allowing mass surveillance and removing privacy, no should be the obvious answer here.