Besides all that, it seems like you simply disagree with the fact that this is a problem at all. If that's the case, we can agree to disagree.
Secondly, I am confused as to what you think should be done. Because it appears that you do not like paying a lot of tax money but expect there to be affordable quality education available?
I mean, if you want more educational options available in your area then presumably that means the government at some level (local, county, state, federal) would have to pay for it which means an increase in taxes (for someone at least).
Third, you did say "Low-income families have a higher probability of raising children in a dysfunctional home who then become a burden on the local school district. " So it seems fair to suggest that you should consider raising the level of your income to meet your desired needs.
Fourth, in all fairness I don't have children so I am not sure why I should have to pay any tax what-so-ever for your child to receive a poor education.
I shouldn't be locked into a specific school based on where I live. If there's a school 20 miles away that I think would be a better fit for my children, I should be able to take them there. Basically, I'm arguing for a free market.
Otherwise what you're suggesting is that you should be able to place your child in a school that you yourself do not pay taxes towards since you're not in that district.
So other people in that district should disproportionately support your child's education compared to what you are?
Because it’s a shared societal good, like government, roads, policing, defense, energy infrastructure, and many other things. An uneducated populace would burden everyone.
Beyond that, unless you went exclusively to private school, you also benefited from the system and it’s not unfair for you to now contribute.