There are many things you can do to rip apart a peer-to-peer network. You start by generating a few million identities. Next, you start manipulating the peer sampling mechanisms to surround nodes with evil peers and create groups of evil peers ready to acknowledge transactions. Finally, you can convince surrounded nodes of pretty much anything (e.g., that the network is far smaller and younger than it actually is) unless they consult a trusted authority claiming otherwise.
Of course, if you had a trusted authority you wouldn't have to go through all this trouble and you could just let it sign a bunch of coins or even handle the full transactions. It would be just like every other currency, and now you know why.
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