Snapchat was based around that and people still copied content.
If someone can read it, then they can copy it.
If someone can read it, then they can copy it.
Most people will not archive all texts they get in the moment, it's only after some fallout or event happens they there's motivation to dig up old messages.
Wickr does "screenshot notification" somehow, so now I occasionally get sent photos taken of phones showing "private" Wickr messages...