[eyegor]

But if everyone used a public blockchain, with proof of work + user-level signatures for each vote cast, wouldn't it be far more auditable than any current system? Ignoring implementation details, reaching a point where anyone could have a way to audit that their vote was counted (correctly) seems very useful. Using this sort of model, it theoretically wouldn't matter who completes the proof of work as long as the results are audited.

[baobabKoodaa]

You don't need blockchain to enable voters to verify "that their vote has been counted correctly". Several cryptographic voting schemes already provide this feature (for example, Civitas and Floating Receipts).