Maybe the internet isn't forever after all. New services are popping up to enable you to privately share messages with a select few, and to even have them self-destruct at a given time/interval. Some high-profile people with a penchant for sending pics (looking at you Carlos Danger) should Love this. In the era of domestic surveillance and the realization that most tech companies are complicit is this the silver bullet?
Maybe not. Just because it's deleted from public consumption, how long does it take the site's respective crawlers to get it? Accessible and deleted are two different things.
How will FB and Twitter feel about being used less as a publisher and more as a temporary broadcast medium. You might think that's what they were... you would be wrong. The ability to broadcast and store your thoughts, ideas and drunken outbursts for future consumption is a part of their value proposition.
Are their respective graphs as valuable without storing everything? If not look for the API or ToS to change very quickly to eliminate the ability for a 3rd party to delete on your behalf. On the other hand this is a means to combat hot new chat technologies like SnapChat (which for some reason feels it's worth more than 3 Billion)