I guarantee you that if everyone had science/engineering degrees, Netflix would still be streaming movies and television. Just because I am going to school for an engineering degree doesn't mean I won't take a job in the music industry (nor do I need a formal system of education to play good music)
It seems like you've never talked to an engineer, as math is very highly regarded in the engineering world as it allows engineers to do most of what they do. On top of that design is also very highly regarded in the engineering world, as most of the things 'created' by engineers are 'designed' by engineers. Your senseless disconnect between science and math (and strong connection between math and liberal arts) is a whole other debate that I don't ever want to go into.
I can't even imagine hearing a respectful engineer talk down on computer science (or software engineers), I haven't met an engineer that has done this yet. In fact, most of the engineers I know started with computer science and then moved onto things such as ex. electrical engineering or mechanical engineering (and even vice-versa!)
You are also making the assumption that the entertainment industry is built off of people with liberal arts degrees, when it is exactly the opposite. The people who built the entertainment industry were people who had a burning passion.
I'm trying to make the point that design and engineering are practically the same thing.