It is the defendant's right, not the state's, to have a jury trial.
If an accused has the right to waive a jury trial, he has that right. I don't see why there should be any issue. It is the accused, not the state, which has a right to a jury trial.
I trust the source, Martindale-Hubbell, and it clearly states the defendant can waive and opt for the bench trial. And that sounds right.
I hope you are right. While I don't know the law well in North Carolina, it is not the universal view. And Martindale-Hubbell is not a source, but a summary put together by non-practicing lawyers.