Would save data for the website and allow users to reference old messages and PM's which they don't necessarily want on the website anymore.
And what's to stop me from referencing an old message that actually never existed?
I assume you mean quoting old messages.
The point of this feature would be to keep a backup of old messages in case you need to access what was said months later.
Sort of the same thing as deleting emails on a email server, but backing them up incase you need to see what received/sent back in the day.