I thought that the blockchain (itself) afforded some anonymity, while still preserving trust, through cryptographic signing.

Which sounded beautiful, until I realized that there must needs still be some other market around the blockchain, in order to interface with reality and older currency systems. There, all privacy bets are off.

Thus, even if one wanted to conduct and election, and put all votes on a block chain, maintaining a secret ballot seems impossible, as far as I can tell.

Sometimes, a primitive solution like a paper ballot has crucial superior aspects.