Is it feasible to self-study all the courses of mathematics major (undergraduate system) in universities?
I think there is no problem with your ability, but I don't think it is necessary. Mathematics majors focus on proof and so on. For non-mathematics majors, as long as they can be applied, it is enough. There's no need to figure out the proof or anything. Mathematics in general science and technology education is enough. The recommended Introduction to Advanced Mathematics compiled by Chen is particularly good, concise and profound.