Judges have a huge amount of leeway in deciding on supervised vs. unsupervised visitation.
When I got custody of DS#1, ex-h was awarded every other Sunday 9-5 supervised by ex's parents. It was easy for me to get this, but there are reasons for that. I don't think it's usually that easy. The circumstances were:
1) Ex-h has 2 children from a previous marriage that he did not have custody of. He was entitled to visitation, but he was inconsistent about it. There were a lot of reasons for that, and I can honestly say that many of the reasons involved his 1st wife who had issues. LIke, her issues have issues. He does not see his children from his 1st marriage. (In fact, I recently reached out to his 1st wife because DS#1 has been begging me to see his older brother and sister. She was sort of nice about it, but told me no. Then she went into some bizarre story about our mutual ex beating on their daughter and her son having to break up the fight, during some visitation that must have happened some years ago... I mean, it's like she took the train to crazy town and got off. I am no big fan of my ex-h, but I never saw him do anything like that to any of his children. I suppose it's possible, but frankly he's just too lazy. He'd sooner let his kids do whatever they want and not have an argument about it.)
2) I had a protective order that he agreed to, and this was the visitation set forth in that order. Therefore, I had a precedent of a visitation arrangement (day, time, and supervision) that ex-h had already agreed to. My lawyer just asked the court to continue it.
3) Ex-h had been in this family court several times for non-payment of child support for his children from his 1st marriage. One judge had put him in jail, and my ex-h created an ugly scene. My lawyer filed my custody papers on a day that guaranteed that I would get this same judge for my custody case. Frankly, once my ex-h name showed up on the judge's bench, I was going to get anything I asked for.
4) I'm pretty sure ex-h didn't show up to court because he had some outstanding warrants, so he really couldn't argue anything.
But the reasons I wanted supervised visits were a little different. Ex-h has never been abusive to DS#1, although he became abusive to me right before our marriage ended (he laid his hands on me once). The supervision was so that I could drop off and pick up DS#1 with my ex-in-laws and not have to deal with my ex. Also, while ex-h is not abusive to DS, he is... like, flighty. As in, I knew my ex-in-laws would make sure that DS#1 was bathed, fed, etc. Even though he is only guaranteed every other Sunday, he's allowed to see his dad and grandparents whenever he wants.
Things are much better now, although we have had our ups and downs. When ex-h was homeless and living in a motel with a stripper, DS#1 wasn't allowed to visit him there, although he could still go to his grandparents. Now, ex-h lives with wife #3, and I trust her, so DS#1 can spend time at his grandparent's or his dad's, whichever he wants (they live very close together).
My order was put in effect in 2006, and I've never had it changed since it gives me full legal and physical custody. Since DS#1 visits to his dad are still de facto supervised by his grandparents or his stepmother, and he's old enough now to find food and shower (LOL), I'm really flexible with visitation.
As usual, talk to a lawyer. Also keep in the mind that if supervised visitation is ordered, who has to pay for it? I don't know, and I avoided that issue because his parent's were willing to supervise.