My mental analogy is based on the print edition, where I can clip an article for my files, and find it years later. If I can't make a persistent link, then what's the use? I call papers that do this "Newspapers of Non-Record", and I think they're "shooting themselves in the foot".
I'm aware of their need to pay bills, etc, but believe this is a very counter productive method. At the same time, I'm not at all sure what the papers *should* do to recoup costs. I