Ultimately, though, what matters is experience and skills. Again, in law and medicine, the only way into the profession to gain the experience is to have the degree. That's not the case in the tech world.
I also have a different perspective from you on STEM degrees. It's true that tech has a "lower barrier to entry" if all you look at is official, legal, licensed barriers.
But majoring in STEM fields is vastly more difficult than a major typical of a law school graduate, and elite STEM graduate programs have vastly higher attrition rates than elite law or medical schools (like, 50-100 times higher). The coursework is exceptionally rigorous and difficult.
The difference is that you don't strictly have to do this to go into high tech - lots of people don't. And that's great. But then, again - why is Obama pushing STEM?
http://www.nytimes.com/2014/08/03/education/edlife/how-to-le...