Yes, there are many facets to the problem.
However, if you read the link to what the Australians are doing, you will see how they will be using BCT to ensure “one-voter, one-vote”, as well as security in electronic transmission. One might ask why the Australians are so concerned. The answer is in their geographic location. They are susceptible to hacking from China, India, Indonesia.
As for the illegal voting problem, that problem should be lessened by the policies of the Trump Administration. If they are not here, they can’t vote unless they are still on the voter rolls, and in that case, those rolls can be scrubbed. So over time, the illegal voting problem should wane.
The BCT is optimal for ensuring secure transmission. As stated in the first post, even where paper ballots are used, the results are still at some point uploaded electronically.
The blockchain is a secure ledger. All the transactions are signed with someone's private key and contain the public key so the signature can be verified. That's all the security it has. There's no secrecy of any sort, nor authentication other than signing with a personal private key. So uploading ballots from some other source (e.g. paper) will require something new.
I can't create a entire secure upload on the back of an envelope but there would have to be a private key involved. One way to do it (again subject to real security analysis) is to print a private key on each paper ballot as the vote is cast by a voter verified by their ID in person. To upload the scanner will read the private key and use it to sign the transaction containing the ballot. The total number of transactions can't exceed the vote count for the precinct.
But there could be extra ballots from the trunk of a car substituted for real ballots. Normally a private key is on someone's electronic device and the corresponding public key has been registered using the voter's identity documents. In this case the computer in the precinct that creates the private keys has to print out public keys. If those printouts can be stored securely with the paper ballots.
If there is an audit or recount the ballots can be hand counted and the public keys can be checked against those on the block chain to make sure they match.