"Stuff school should have taught me" material is actually stuff your parents should have taught you.
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.
I would argue that your points about kids not caring and forgetting information are not inherent to the concept of education, but to how most places do formal education.
Humans learn best through practical examples that affect their lives, and through doing things. Sitting people down and giving them information, and then later having them regurgitate that information, is just not the best way. It's cheaper, it requires fewer teachers and fewer resources, but it is not the most effective.
Yeah, and some practical concepts are going to require knowing abstract concepts. A lot of accounting is just algebra presented with words instead of letters for variables. Understanding compound interest requires understanding exponents.
And the duality of "why do I need to learn this" and "why are they teaching me this" is to push off personal responsibility for the education. Real life has a lot of these tests that come up at random and require specific information, requiring different forms of puzzle solving. And they teach different methods of puzzle solving in school.