There's still a tremendous amount of trust involved, and many components to secure. Some folks have done security analysis of voting machines and were not impressed (an understatement). Block chains and other applications of crypto are kind of pointless if the firmware can be subverted to record Candidate B while displaying Candidate A to the user.
Oh, there are lots of technological solutions (display hashes of a vote, which can be photographed and checked, for instance). But paper and pen have worked for a long time and we have decent strategies for dealing with its faults, while the target area of a microprocessor-controlled voting machine is mind boggling.
That doesn't preserve the anonymity requirement for safe voting systems. Blockchains are only pseudonymous and a malicious landlord, employer or family member could easily coerce you into divulging your ID.
If you take the key with you after you vote, which you will need to do if you want to validate your vote later, then you can be coerced into disclosing it.
I believe that the keys would just be taken by the machine, that way you'd be able to verify the vote was placed without the risk of revealing the identity of the voter attached to that card.
Oh, there are lots of technological solutions (display hashes of a vote, which can be photographed and checked, for instance). But paper and pen have worked for a long time and we have decent strategies for dealing with its faults, while the target area of a microprocessor-controlled voting machine is mind boggling.