Tradition. Math as we do it goes back to the original Academy, the one Plato started. For most of its history, math was all about the mathematician, you studied math because studying math made you better. We didn't even start thinking about applications in math education until the industrial revolution meant we needed factory workers who knew a little math and it was just assumed that you didn't want to try to teach the proles how to think. Math academia is weird to me. In physics, researchers insist that there are applications to even esoteric problems, often to a fault. Mathematicians,on the other hand, often get offended at the idea that math needs to be created to solve other problems, that rather, math is done because it is elegant and beautiful, and if it happens to be useful to someone outside math that's just an unintended side effect.
It also seems wrong to me that the author finds it useful that all he got from his education is problem-solving ability. That is ignoring the fact that in another major he may have learned that same problem-solving as well as helping the world in a pragmatic way. They aren't mutually exclusive.
Only slightly related to the post at hand, but I'm a bit curious what generally motivates people into going into a Masters or PhD program. I stopped my education at the Bachelor's level specifically because I couldn't actively justify what I would need either of the two for outside of monetary incentives. Especially with the push I felt during my undergraduate career towards getting kids into 4+1 or accelerated Masters programs... I wonder if the case of this article isn't all too common in other fields. Or maybe that's just me projecting.
Probably depends on the field. In my field, computer science / software engineering, the consensus is that a Masters will make you a better engineer, but a PhD isn't really useful outside academia. I imagine there are fields (chemistry maybe?) where a PhD is useful in the field. I do think my Masters made me a better engineer. I learned more broad knowledge like graphics and architecture, and I picked a specialisation, parallelism, which is imminently useful.
Funny, in Chemical Engineering it's almost the opposite. A Masters won't get you much farther than a Bachelors but a PhD can open a ton of R&D doors depending on what industry you focus on.