Note that I specify provider above. Twitter is somewhat useful, but that is despite of, not because of the interaction design of it.
Edit: IIRC app.net was a bit overpriced and had some weird limitations too, although the latter might just be me remembering that they copied all the design mistakes of Twitter for no good reason.
Edit2: If anyone is in doubt at all: Twitter is popular because of the network effect. Everything else has been solved better by one or more competitors.
What I hate about FB or Instagram is the "look how great my life is" aspect.
Privacy in social media is a feature that is bound to self-discipline of the service provider
A company could provide terms of service and perhaps an explicit creative works agreement defining the exact uses for which the company will use the data (to display on the website, to comply with legal requirements, etc).
It would still ultimately rely on a whistleblower or voluntary auditing, but the combination of clear damages and a not-open-ended terms of use would keep the company lawyers invested in keeping the company honest perhaps.