Another non American here.
Swearing on the Bible or God is an oxymoron or paradox in court as it is supposed to be beyond reasonable doubt.
I've affirmed in court on several occasions and rejected the Bible as being without evidence. That wasn't lost on the jury as they are making a judgement based on evidence and if they themselves believe in a god without evidence then they are not fit to be judgemental.
However I was only a witness and not the defendant.
I had to swear on the bible during my divorce years ago. Even though things were going clearly in my favor I did not want to take even a tiny risk of not getting custody of my kids. I live in the bible belt.