No, they should not.
It was a proud tradition with strong historical roots, which could have been democratized and spread to incorporate women and working class males. Legalizing duels under supervision of police officers would reduce crime, help settle scores and matters of honour, rivalry etc.
Sorry, but this makes me sick. There are other ways of settling problems and disagreements than violence. And no matter how you "supervise" and "democratize" it - a duel is an act of lethal violence. I wouldn't want to live in a society that settles "rivalry" by killing or even hurting each other! Haven't we overcome this frame of mind?
Not that I'm surprised, though, watching the gun control debate in the U.S., with people who claim the right to own tanks.
Still hope this thread was intended as a joke.
Pessimism is usually the best option when it comes to human nature.