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 if we, as a society, make it a habit to offload our morality and wisdom teaching onto the schooling system, we're going to end up with no more parents at all; just breeders who ship off their kids. I'm sorry your parents were terrible, but that doesn't mean we should force every school to pick up a curriculum for everything.
Which one would be easier to change? Every parent, or the educational system?
It would be easier to change the educational system, but our society has grown so gluttonous for shortcuts that I can't recommend the easy way here.
Better question, do you want the least educated among us teaching what's not currently in taught in school? Cause that's what you're advocating.
Now it's obviously not all parents, but the point still stands. The better educated parents are already doing something to teach their kids what's not in the curriculum, but even amongst them it's still a small percentage.
Including things like basic taxation and financial education, the voting system, stuff like that. Make it mandatory to go through, if not actually have a passing grade.