With a blockchain, you could verify that your vote went through but so can your neighbour. Even if you find some way around that: If you can see how you see how your vote was counted, you are able to prove to someone else how you voted making vote selling possible. These are two big reasons not to use such a system.

Personally, I know for certain that my vote in the last election went through because I have seen the complete process myself and have verified that the published vote counts match the once counted in the polling station. There is no black box left.