You might need a database of citizenship, perhaps database of other validity criteria like renters and homeowners. But those are not voter databases. The blockchain eliminates the voter database. The registrar uses those other databases which are maintained for other reasons, mainly tax collection, to look up legitimacy. Then the registrar places a hash of the voter's info into the blockchain. Note that blockchain is not a database.
Does this solve the problem of a voter registering twice under two different identities? Heck no. College students could register with their home address and do it again with their college address. The blockchain will make it easier to cheat and do that since it will be harder to check for potential dual registration.
Right now there are voter databases and they can be compared to see if a name comes up in both. Then that name can be investigated further since different people might have the same name and therefore could be legitimate. What would happen with blockchain? Well there are no databases of voters to compare, so we can't do that. Instead we would have to create hashes of possible student names and addresses and check every state or locality blockchain to check for matches. Very difficult even with canonicalized names and addresses.
These are hard but not impossible problems. The good part is that the blockchain is immutable so if we get lucky and find cheaters we can prove that they cheated.
No you need a VOTER database. Remember to be eligible to vote there’s also age requirements, not having been convicted off a felony requirements, of course if you have been convicted you can sue to get your rights restored, residency requirements, still being alive requirements, and of course FINALLY you actually have register to vote. Registrars have a database right now, the job cannot be done without it.
And again you admit your system doesn’t work. It’s funny how much time you put in insisting your system while admitting it doesn’t.
I’m not saying it’s an impossible problem. I’m saying it’s a problem that blockchain does absolutely nothing to solve. It’s the wrong tool for the problem. We’re trying to drive across the country and you’re insisting the tool for the job is a shotgun. A shotgun could be helpful, there might be something that needs shooting, but we lack a car, and all the shotguns in the world ain’t fixing that.