Standard disclaimer first: I am often wrong.
But I've got a nagging feeling that all of the pure Proof-Of-X (where X != Work) systems would set up a dynamic of "the rich and powerful get more rich and more powerful."
The more coins you have, the more you get, as far as I can see in all of the proposed schemes (another disclaimer: I only vaguely pay attention to all of the Proof-of-X schemes, so feel free to tell me how I'm wrong). Seems to me that would end up being a destructive feedback loop, where your decentralized currency naturally gets more and more centralized over time.