Schools shouldn't be treated as these magical places where you're put in at some age and over a decade later you emerge a complete human being. You have parents and you spend more time at home than at school for a reason: you're supposed to learn from your parents.
A school can potentially give you a degree of financial literacy instruction. Your parents should be the ones paying your allowance money and driving you to the bank to get your first checking account. A school can teach you how to cook something. Your parents should be the ones eating your food and helping you cook it better. A school can show you some level of DIY. Your parents should directly benefit from teaching you how to fix the sink when it gets clogged. A school can tell you what kinds of careers exist. Your parents should love you enough to tell you that either your career ambitions or your financial expectations need to change. A school can tell you how to build a resume. Your parents should be the ones driving you to your job interview and to your job until you buy your first car. A school can give you a failing grade when you do poorly on a test. Your parents should be able to make you face the real, in-the-moment consequences of doing something wrong.
Expecting a school, public or private, to teach you everything you need to know is a grave mistake. You need people in your corner who are taking an active part in raising you all the way to adulthood and beyond. If you have kids yourself, that goes for them as well. If you aren't there for your children, to teach them the things that schools don't teach because they can't mass produce the lessons to nearly the same quality that you can give them, they'll blame you and the school for having failed them. And they'd be right to lay the blame at your feet.
And what if one has shitty parents?
And what if one is only able to visit a shitty school?
Your right though, one should have easy access to good education no matter what kind of home they are from.
Public policy can/should fix shitty schools. You 'just' need funding, staffing, and leadership, plus to some extent a willingness to ride roughshod over parents who willingly avoid teaching e.g. science, sex ed.
Public policy can only do so much about shitty parents.
Schools are a societies responsibility though. So I can try to create better schools for all while trying to create better parents... Oh wait I'll taggle that with better social support systems and educations for future parents as well!
Good schools rock!