A good CS education will give you a wider perspective, a stable foundation to build on. Then you need practice, lots of it, to become anything close to competent. But being able to orient yourself and having been exposed to several different kinds of problems and languages, and learned an algorithm or two, definitely helps.
One of my university teachers told us that to become a real programmer, you have to design and build at least one language of your own. I wouldn't choose the same words; but having done several, I sort of agree. You need practical experience before it makes any sense though.
University industry, unions, and academia more broadly, set the tone that if you want to do anything "for real" you must go to school. Many companies, parents, and ordinary lay people are convinced.
My (somewhat limited, I am young) experience tells me that competence is a completely inadequate predictor of whether somebody went to school for computing or software, but self-importance is an excellent one.