Seems like a good explanation to me.
I'm not quite sure I agree that most middle names in the USA were originally the maiden name of the mother, however. It seems to me to be a bit more complicated than that. The first US President to have a middle name, John Quincy
Adams, was given the maiden surname of his maternal grandmother as his middle name (his mother's maiden name was Smith). A lot of the examples of early middle names for boys are when the boy was being named after a particular person, either a national political figure or a family friend, and the middle name was the namesake's surname. John Quincy
Adams himself had a son named George Washington
Adams, for example. I think the impetus for that was to clearly designate that Washington
was the person being honored instead of some other George
. Often in the early days when the son's middle name is the mother's maiden name, I think it's because the child was being named quite specifically after the mother's father or brother, and it was only gradually that the idea of using the mother's maiden name as a sort of "generic" middle name option developed.