I also could have voted twice, if i wanted.
Absent of a national register, there is little that can be done. That is just the way laws work. Laws do not prevent someone from doing something illegal, laws, with few exceptions, provide a way of punishing people
after they do something wrong. The intent is that the punishment after committing the crime will discourage people from breaking the law. Whether this works or not is debatable.
There are no laws that prevent you from murdering someone. There are, however, laws that outline what will happen after you commit murder. No law will prevent someone from committing a crime. If they could, our society would be a lot better.
There are laws against voting twice, but realistically, they can only be applied after the person has voted illegally. The problem is that after the person votes, there is little that can be done to nullify that person's illegal vote. Provisional ballots are the only way, but we can't run elections using only provisional ballots.
It is a delicate balance. We want the freedom of a secret ballot, but at the same time we want accountability concerning voting. Finding a compromise, and everything ends up being a compromise, is an imperfect art.
What we want is a system that is secure "enough", convenient "enough", and cheap "enough". Oh yes, costs are an important factor. If we are not going to compromise, we have to pick one at the determent of the others. I can devise a voting system that is 99 +many decimal points secure. But you would not like the convenience and certainly could not afford the cost. It is easy to devise a voting system that prioritizes any of the three at the determent of the others. But that's not the ultimate solution.
Either an interstate register, run by the states, or a national register, run by the federal government, might be a solution to this.
There is a lot of resistance against a national registry.
The states, so far, have not been willing to cooperate with other states on this issue.
Despite the warts, I feel that we do a pretty good job with our elections. Not perfect and there is plenty of room for improvement. But overall, a good compromise that we should be proud of.
We have 50 states and some districts/territories who don't really talk to each other but somehow we manage to elect idiots to office.