The "peace of mind" reason can go both ways. A lady in my church did not have an US with her first child and had an uneventful birth and a healthy daughter. She did have an US with her second and was told that he had water on his brain and that he was too big and she would need a c-section. Needless to say she had a very bad rest of her pregnancy (she didn't believe in terminating and imagine if she had! She said the thought just chills her bones...) and when her son was born via c-section he turned out to be a whole pound smaller than his older sister had been and there was absolutely nothing wrong with his brain.
That particular mama could have avoided a lot of unnecessary stress and an unecessary c-section had she NOT had a routine US with her son.
Then again, my mom found out that her third baby had a diaphragmatic hernia from a routine US and, though he didn't survive, she was able to have surgery on him in utero and was spared having a full-term still born child. It was still traumatic and didn't change the outcome, but it could have potentially.
So really... "peace of mind" doesn't just argue for having the US. I'm more at peace trusting my body and not seeing something potentially abnormal on a screen that may be nothing at all. Spending the rest of my pregnancy worrying about something that may have been a sonographer's error is not something I want to deal with. I wouldn't terminate a pregnancy regardless of what the US showed and I would fight to have a home birth regardless of what the US showed (due to serious needle and hospital phobias which I could imagine would interfere with the birthing process a bit...). It's just not worth it to me, personally.
I will only be having an US if my midwife recommends one, and she knows that I would do it if she thought it necessary. No routine US for me though.
But that's just me
I respect the right for all women to make an informed choice about this and all other issues relating to pregnancy/birth since the comfort level of the mother is so extremely important
love and peace.