You make a good point about paternity suits. They were around.
However the statement “This acted as an inducement to get married before having children” seems to me to make perfect sense.
In the same way that the 1960’s supercharging of preferential and “per child” welfare for unmarried women with children undercut the structure of the American family...
...if a woman must marry a man in order to be assured of financial support from him, it encourages the woman to NOT have sex and get pregnant until the man demonstrates his committment to their family through marriage.
It was one more thing encourging marriage and families that was intentionally broken, mostly by “Democrats,” in the 1960’s.
The OP stated that there were no such things as paternity suits prior to 1972 - and that that fact acted as an "inducement" to get married before having children.
But insofar as we have established (or agreed) that there were indeed paternity suits prior to 1972, then that means that there was, in fact, no actual "inducement" to get married before having children.
If women had had no legal recourse, then indeed that would have been an inducement - at least to women - to marry first. But that is a purely hypothetical argument.
Regards,