It isn't just about how much money you spend, it is also about how the money is distributed, which actors get it and what they spend it on.
If state governments took over control of schools and local school districts were abolished, that might well not lead to any change in the overall amount of money spent on public education, but it would very likely lead to changes in how and where that money was spent.
I agree that changing funding models can’t address broader social issues. But at least the school can reach out to the parent(s) and say "your child is skipping school and failing", which this mother claims they did not. Either the mother is being untruthful, or else the school really did fail here in a way which is independent of the social issues of the child and their friends and family. And if the later is the case, changing administrative and funding structures might actually make some difference. Not to the ultimate problem of the child's social deprivation, but at least to the parent(s) saying "we had no idea".
If state governments took over control of schools and local school districts were abolished, that might well not lead to any change in the overall amount of money spent on public education, but it would very likely lead to changes in how and where that money was spent.