Literally every story you posted involves the biological father not being listed on the birth certificate (one even listing the non-biological father), resulting in a default to the husband.
It's got nothing to do with dating single mothers and everything to do with not marrying someone with children who don't have father on their birth certificates (some states even specify that you must be married when the child is born to be stuck with child support).
Quit Google searching clickbait titles and do your research. Dating women with children won't suddenly get you child support.
First, how are these clickbait titles, when it is all documented? Second, did you not see the last link with a quote?
https://family-law.freeadvice.com/family-law/child_support/Child-Support-for-a-Child-That-Is-Not-Mine.htm (child by consent section)
"Laws favor someone being named the father because they do not want a child going through life fatherless. The equitable doctrine of estoppel applies to persons who have for all practical purposes consented to being dad, regardless of paternity. The basic theory is that since you acted like a parent and permitted the child to believe you were their father, the child now has a right to rely on your representation that you are their father. "