If there's literally no value in taking it over, then why password protect it in the first place?
I have an online photo album and while I could password protect it and share the password with people that I want to share it with, there's very little value (perhaps there's some small social engineering value) in protecting it. If there's no value in exposing it, why bother password protecting it?
Did you mean that it's valuable enough that someone should protect it, but shouldn't bother protecting it too much (like, anyone with the URL should have access to it) since it has little value? I'm not sure I really understand the nuance, but I'd be awfully surprised if I forwarded an email to someone from OKCupid and it gave them passwordless access to the account.
Even at a lower level, just sending a bunch of messages asking for money for a cab/train/airfare might yield good returns. People let their guard down when there's a possibility of getting laid.