I would posit that an opposite movement will also happen. Social networks become more ubiquitous but that very ubiquity will teach people what not to share and raise the value of the "anonymous web".
For example, if a merchant can understand their customers exactly, it introduces an information asymmetry into the market game that the merchant enjoys but I, as customer dislike. I don't want a merchant to know exactly what I'd be willing to pay for X. I want the merchant offering prices anonymously and then for me to be able to pick the best of those prices.