Snapchat was based around that and people still copied content.

If someone can read it, then they can copy it.

it more so prevents people from retroactively going back in time and scraping data they wouldn't have in the moment. Many of my chats expire all messages after 24 hours because of this.

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.

Yep.

Wickr does "screenshot notification" somehow, so now I occasionally get sent photos taken of phones showing "private" Wickr messages...

In order for the message to be readable by the other party you fundamentally trust the other party. A self-destroy timer doesn't really help that aspect (which is why I don't use them).