The vast majority of people who are paid to use their knowledge of mathematics aren't doing math research. In fact, mathematics research is so uneconomical that most mathematics researchers spend 20%+ of their job on teaching.

The number of people who are paid a full 12 (or even 9) month salary to do mathematics research is vanishingly small.

> This problem is accessible to anyone who knows basic high school algebra, but it requires a lot of effort

That effort is really difficult to get out of students because few students have intrinsic motivation, and there's very little extrinsic motivation (unless 3 post-docs is your idea of a good way to spend your 30s...)

I'm not sure what the solution is, but showing more people what mathematics researchers in universities do with their non-teaching time seems like the wrong solution.