Voting seems like one of the few problems that blockchain is actually the solution for.

Nope. Blockchain has no anonymity.

You don't have to attribute any name to the transaction, just a voting booth ID and the vote. The actual benefit is just that it is hard to tamper and easy to trace where tampering happened.

But I still prefer the paper vote and I usually a blockchain apathetic.

Monero demonstrates a solution (https://en.wikipedia.org/wiki/Ring_signature)

wouldn't that be a feature in this case?

Anonymous voting means that you can't sell your vote. Like, if I pay you $5 to vote for X, but I can't actually verify that you voted for X and not Y, then I wouldn't bother trying. Or if I'm your boss and I want you to vote for X... etc.

Not really. Your ballot should be secret, which goes against blockchain, I guess.

The blockchain doesn't require your ID, just the voting station ID.

Any id can be correlated.