Because of the Great Society. The rules for Hispanics are no different than the rules for Blacks which also broke up their family units. Amnesty does away with the need for anchor babies and I believe that this will also have an effect on out-of-wedlock births.
You're totally wrong about that. Anchor babies have nothing to do with amnesty or no amnesty, but are an interpretation of the constitution that any child born on US soil, regardless of the parent's citizenship, is a US citizen. Parents could still enter the US illegally, present themselves at a hospital, and have their anchor baby delivered at taxpayer expense.
There are other anchor baby parents who arrange vacations to US, come here from Asia or other non-Latino parts of the world, have a 'US citizen' child, then return to their home country with their anchor baby. They do that just in case things become untenable in their home country in the future.
The only thing that will end the anchor baby scam is a change in how the constitution is interpreted, by the courts or through new legislation that stood up in court.