Might not be a bad idea for the state to say “Every ballot must be uniquely identified”. When you show up at the polling place, show your voter ID, they hand you a ballot, you vote and you leave. That would be an anonymous system, and if that is important to a person, then showing up at the polling place would be the way to go.
Of course, if anonymity means nothing to someone, they can mail-in their unique ballot. And, yes, mail-in ballots could be tracked and we could know How people are voting. Some won’t mind — but for those who do mind, that’s what those polling places are for.
Agree, there are ways to use serial numbers...but also ways to abuse the system. So people do have to be careful.