I'm from the U.S., so that's what this post is based on. Unfortunately I don't know much about education systems elsewhere, but I really should do some reading on them.
As someone who plans to become a college professor: yes, the school system is flawed. The lack of teaching of essential skills; taxes, cooking, things like how to change a tire, should all be taught in a sequence of courses beginning at the very least in the last year of middle school and continue as long as needed, but ending in high school before college. It's far more important than old literature and, even as someone who specifically wants to be teaching math, I have to admit those essential life skills are far more important than math. I mean you should know how to add, subtract, multiply, and divide nonnegative rational numbers without a calculator, though.
There also needs to be less emphasis on being a well-rounded jack-of-all-trades, most especially in college. As a math major, taking courses in world history and English literature are a complete waste of time. Similarly, someone majoring in history or English literature is completely wasting their time taking STEM courses. College is expensive - I want to be spending that money on courses that further my career, not on courses that I don't need or want. My college requires 6 gen ed classes for my major. Without those useless courses, I could graduate early and move onto graduate school sooner, moving closer to the career that will actually be paying the bills. Everyone could, actually! Most majors in my college actually require 9 courses, 3 extra in foreign language (my other 3 are replaced by very useful and practical comp sci courses). I don't envy those who need 9. If people want to take courses outside their intended career path, or are still undecided, then that's totally ok! You should still be able to take courses in areas of interest. I'm getting a CS minor, so I'm certainly doing that; though CS and math are closely related. But don't force gen eds onto people. It's useless.
I will say that everyone needs to know how to write. That's very important. No, not English literature, that can be in other courses not required for all majors. Writing and research. Technical writing. Styles besides MLA. That's the stuff you gotta know.
The credit system. What's considered full-time should not be based on credits, it should be based on course difficulty. I know different people can find different courses difficult, but there comes a point where everyone can reach an agreement. Four 3-credit, 100-level courses won't be as difficult as four 3-credit, 400-level courses, no matter what major you're in. They shouldn't be seen as the same load. They aren't. You need to spend more time studying with the latter load than former. Contrary to the commonly held belief, credit load does not ever, ever equal how much time you need to put into a class. What is it, 3 hours out of class a week for studying per credit? Yeah, right. As if a pre-calculus course and a real analysis course are in any way, shape, or form comparable in how difficult they are by credit load.
Teachers are an issue of two points. For one, they certainly aren't payed enough. Especially when I think about elementary ed teachers, wow what an amazing and patient person you have to be to deal with all those small children! It takes some real skill to do that. All teachers, really, they need some fantastic skills. Not only do they need to have completely mastered the course material, but they need to be able to communicate it to others. They need to have top-notch interpersonal skills - I'm still working on that one the most. Teaching should really be a high-paying job.
The other point? There's a lot of teachers out there who shouldn't be teaching. It's not what they're strong at. This is also an opinion thing - one person may think a teacher is the best, and another person may think they're the worst. But there's certainly teachers that seem pretty darn unanimous in how students feel about them. Good STEM teachers, particularly math, can be very difficult to come by.
I never went to public school, so I don't feel I have a good handle on what to say about that. Honestly it doesn't feel like it's my place to be saying anything on the topic since I never experienced it. I can only say, based off of anecdotes I've heard, that there needs to be serious changes in them.
Apologies for any typos, weird sounding sentences, etc. I'm very tired, but also can't sleep? I don't get it, humans are weird.