While the Internet was conceived as a decentralized network, the most widely used web applications today tend toward centralization. Control increasingly rests with centralized service providers who, as a consequence, have also amassed unprecedented amounts of data about the behaviors and personalities of individuals. Developers, regulators, and consumer advocates have looked to alternative decentralized architectures as the natural response to threats posed by these centralized services. The result has been a great variety of solutions that include personal data stores (PDS), infomediaries, Vendor Relationship Management (VRM) systems, and federated and distributed social networks. And yet, for all these efforts, decentralized personal data architectures have seen little adoption. This position paper attempts to account for these failures, challenging the accepted wisdom in the web community on the feasibility and desirability of these approaches. We start with a historical discussion of the development of various categories of decentralized personal data architectures. Then we survey the main ideas to illustrate the common themes among these efforts. We tease apart the design characteristics of these systems from the social values that they (are intended to) promote. We use this understanding to point out numerous drawbacks of the decentralization paradigm, some inherent and others incidental. We end with recommendations for designers of these systems for working towards goals that are achievable, but perhaps more limited in scope and ambition.