I graduated from high school in 1972. I do not remember women driving around holding babies at the time. I do, of course remember cars with no seat belts.
I also graduated from high school in 1972. I don’t think it was that common for women to drive holding babies; generally they would put the baby on the seat beside them, or give the baby to an older child to hold.
To the end of her days, my mother would throw out her right arm if she had to hit the brakes hard. It was an unbreakable habit from the years when there would be at least one unbelted child beside her in the front seat. Child seats for cars didn’t exist back then, at least I never saw one.
None of us six kids got killed or even hurt in a car crash.