A degree in CS cannot hurt your child, but it is simply not true that it is necessary to be successful. As proof, I do not offer my own 37 year career as a software engineer with a B.A. in Philosophy, but more of my experience with many brilliant people who had similar or less (no degree) formal CS education. This includes architects, compiler designers, and operating systems engineers.
The higher education industry has milked the knowledge economy’s need for smart people to make everyone think they are necessary. And people who went through that also want to feel as though they gained from it by only hiring others who went through it.
Anyone who started in computers early knows that “smart and hard-working” is sufficient, because they lived it and built much of the current infrastructure that allows web programmers to do their work.