The question is extremely broad, since it talks about "both school level and university level learning," and doesn't make any distinctions between students with different levels of intellectual development and maturity. The brain of a kid at age 7 is doing really different things intellectually than the brain of an adult.
Certainly there are people who can self-learn math. For example, Abraham Lincoln rode around the court circuit, staying at lodging houses at night and studying Euclid, which he thought was a perfect model for presenting a logical legal argument. But most people aren't as smart or motivated as Abraham Lincoln, and most people learn most of their math as kids and teenagers, so their brains aren't as developed as Lincoln's was at that point.
I spend a lot of time every week working with my community college students in my office hours on mathematical problem solving. Most of these students need a lot of guidance.
An important feature of mathematics is that it is relatively easy (compare to many other subjects) to know whether or not one's understanding is correct.
For the students I interact with, this is mostly not true at all. Figuring out how to check your own answer is actually a very high-level skill. Few of them have this skill. As a typical real-world example, I have a student this semester who has had two years of calculus, but does computations like this:
Are there ways to check this answer and realize that it's wrong? Of course. For example, one could simplify the result and observe that it's the same size as the number that was being squared, but that doesn't make sense, because we expect $x^2>x$ when $x>1$. Or they could compute $1.5^2$ on a calculator and compare. But this student doesn't have the kind of high-level understanding that would be required in order to think of these checks.
In my experience, the vast majority of people who learn math in school are pretty similar to the student I've described above in terms of their conceptual understanding. Their fluency with computation may be better, but they fundamentally imagine math as a black box, not as something that they can make sense out of. You could call this type of student "concept-blind." Concept-blind students are not going to succeed with self-study.
What is actually probably needed is more interaction with teachers who are themselves competent in math, who give proper attention to conceptual understanding, and who don't let students slide through to the next level without understanding what they're doing. How to make this happen, I don't know. At the K-6 level, there are far too many teachers who are themselves concept-blind. In the community college system here in LA, students tend to shop around on web sites like ratemyprofessor to look for professors who are "easy," which means that they're systematically avoiding the kind of appropriate guidance they need.