States can and do use other means of jury duty selection. Voter registration is convenient, but technically every citizen is legally required to serve jury duty if called by the court, regardless of voter registration status. Your continued citizenship serves as your agreement to this. To avoid it, you will have to leave the country. I'm not saying that's how it should be, but rather, how it is.
As to the first question: no, jury duty is not a service to others. Your jury duty serves to protect your rights too, not just the rights of others.
However, it is unlikely in our current court system that any honest Objectivist would ever actually be selected for a jury. The first thing that happens during jury selection of a trial is that your principles are identified and, if they do not align with current legal requirements, you are dismissed. Typically, if you make it past 2 or 3 juries without being selected for trial, your jury duty is over and you go home.
I have done just that. In my state, 2 courts can call you for selection, if they both dismiss you, you're done. I was first selected for a DUI trial in which I was asked what I thought of DUI laws (upon my answer, eyes rolled in the court). The second trial was a drug trial, and it went over real big when I looked the judge square in the eye and told him that drugs ought not to be illegal, and basically that the whole trial and its expenses, including his salary, were a waste of my tax dollars. Late in the day, I went home with my $14 check.
I think its a bit premature to ask that last question since an Objectivist society is a ways off. Comtemplating something that is not going to happen soon seems to me time better spent on more immediate matters. For example; precipitating the Objectivist society in the first place It's safe to say that courts in a Objectivist society will be far more objective than they are now, such that juries would likely be unnecessary in most cases. Beyond that, I say: there's a lot of steps between here and there, and there's no shortcuts.