interesting account I've been following, has a beautiful picture at the top, from a woman who recently went from broke to an extremely well-paid insurance adjuster 

YoAdriaaan @Adricrump23 I'm just out here trying to make my father proud.

Yes, street corner is not a school. It's "who made you boss? fuck you." Like you implied, on the street corner, everything goes. In schools, there are supposed to be bosses and then minions, the teachers and the students. Conservatives strongly support the bosses and minions model in homes. 

I looked it up, the following idea has been around for more than a century

Celebrating 50 Years of Unity

2020 marks the 50th anniversary of the integration of the National Congress of Parents and Teachers and the National Congress of Colored Parents and Teachers, which make up today’s National PTA.

In 1897, Alice McLellan Birney and Phoebe Apperson Hearst founded the National Congress of Parents and Teachers with a mission to better the lives of children in education, health and safety. In 1926, Selena Sloan Butler formed the National Congress of Colored Parents and Teachers to advocate for children, especially African American children in segregated communities.

As the United States progressed through the Jim Crow era, the Civil Rights Movement and the eventual desegregation of schools and communities, the two associations fought side by side for every child. Following the Supreme Court decision that ended segregation, the associations held their conventions in conjunction with one another and worked toward merging in all 50 states. On June 22, 1970, the two congresses signed a Declaration of Unification and officially became one association.

The unification of the two congresses is an important part of National PTA’s history and the association’s continued efforts to serve and make a difference for every child.

Over 120 Years Strong

For over 120 years, National Parent Teacher Association (National PTA®) has worked toward bettering the lives of every child in education, health and safety. Founded in 1897 as the National Congress of Mothers by Alice McLellan Birney and Phoebe Apperson Hearst, National PTA is a powerful voice for all children, a relevant resource for families and communities, and a strong advocate for public education [....]

The question is why hasn't "Dads on Duty" happened more often and earlier?

I do imagine some schools that weren't haven't violence problems in the school might not look as kindly on such interference? The school has to want it and trust those parents, the school has to grant them the authority that schools have. Authority is the issue, not democracy-everthing-goes-with-everyone-equal.