I see what you're saying now, I was imagining the type of transparency log that's usually run by a single institution and audited by a few others.

Even if every voter gets a hash and can check that their vote is in the log, you still have a bunch of places where a central actor can misbehave: Deciding who gets to write to the log in the first place, rate-limiting or dropping submissions, or running split-view logs in the event that there's not a ton of replication - hoping that wouldn't be the case in an election.

With a (properly designed) blockchain, you at least push those assumptions into a consensus layer with many writers/validators and game-theory penalties for rewriting its history. It's still not magic; but for something like elections, I'd rather minimize the points where a single operator can tilt the playing field, which is why I was thinking "blockchain" instead of "centralized transparency log"