The effects you list are accurate, but they don't really enforce your main point. Just because public schools do mobilize kids out of their bad homes (by making it a parent's legal responsibility) doesn't mean it exists for this purpose.
Schools are a place for kids to learn. It's not a place to get a meal, nor a solution to a bad home life. We ensure we provide these outcomes in schools today but that's only because society/govt has failed to get these things accomplished in a more appropriate manner.
The expansion of the scope of public schooling to include mitigating a broad range of social problems reminds me of how US police have been forced to deal with social issues that they are not really equipped to handle, such as, mental health, child welfare, drug addiction, other poverty adjacent problems, or the like.
There should be another agency directed to dealing with these out-of-scope issues. Because actual education efforts and funding gets diverted to dealing with the social issues rather than providing education.
Schools are a place for kids to learn. It's not a place to get a meal, nor a solution to a bad home life. We ensure we provide these outcomes in schools today but that's only because society/govt has failed to get these things accomplished in a more appropriate manner.