Over the past 5 years I have taken my kids alone to the US to visit my family, and I have never needed a letter, this summer I took both kids on my own and stayed for about a month. I say no, but if you feel more comfortable with a letter, get one. I was never asked for any sort of proof or a letter any times I have travelled alone with them. I also have a different last name than my children do.
These are just my experiences.