Not really (or at least you would lose privacy part), one reason why voting is anonymous is to prevent 1) intimidation 2) paying people to vote in favor of specific issues.
If block chain would be used it would be easy for someone buying votes to verify that the people who got paid voted in certain way.
It's possible. But yeah, like you said, if your identity was linked to your address or hash you'd lose anonymity.
You'd have to really trust whoever was keeping the records to have a secure db which we know is basically impossible and could allow for coercion if a malicious actor got hold of it.
However if this problem was solved, it would allow for cryptographically provable elections.
I don't understand why you were downvoted. Your question is valid and relevant. There are problems with the current election process, that were evident in the primary elections. There are many manufacturers of e-voting machines, but these are opaque, proprietary and possibly hackable (as has been demonstrated in past years by security researchers). With current wave of interst in blockchain technology, there are several new ventures that are exploring blockchain as an immutable, authoritative record or log that cannot be hacked. The problem is that it is too transparent (people may see who you voted for, not just that you voted). But I think this problem can be solved, and will likely be solved. It may take a few years.
If block chain would be used it would be easy for someone buying votes to verify that the people who got paid voted in certain way.