Yeah, but often (usually?) the woman's maiden name replaces her middle name. E.g. Jane Elizabeth Doe -> Jane Doe Smith. I'm pretty sure my mom's maiden name is printed on her driver's license, paper checks, etc.
Maybe you just didn't realize it, because it isn't very common to see someone's full name? It was very much the norm until the 80s-90s, and even today I think the majority of women still go that route. I just spent a couple minutes searching Facebook to sanity check myself, and so far all of the women I'm friends with who are under 30 and married have done it.
I wouldn't use Facebook as a guide. My sisters all have done <First> <Maiden> <Last> for facebook, but none of them have legally changed their middle name. They just do it on facebook so that people can find them.
Most if not ~all of those women are doing it so people can find them on Facebook, and people in the States rarely use the middle name field anyways except for legal docs.