Schools should (and are) be places where new stuff gets made up. Google was a project at a university, so was Facebook,.
University, yes. But even then only really after the Bachelor's level. You need to learn to walk before you can run. The problem of exams and problem-solving skills applies to high school and elementary schools just as much as it does to universities.
You can't "be creative" in a subject without understanding the basics. And universities and schools still need a way to test if you understand the basics.