Am I to understand that "engaging with mathematics" is to mean that the only useful contribution anyone can make is furthering the state of the art? If that's the case then yes I can see why it's so rare.

However if we broaden the scope of contribution we can see people finding applications for theory in industry as useful. It is useful to revisit pedagogy in order to bring more people into mathematics. Even people who take the role of Martin Gardner and bringing mathematics to laypersons is a good contribution -- it gets people excited about the developments of mathematics!

What I have learned has improved my life and made my work better. I think that's useful.

update

I have an inkling as to how vast mathematics is. I realize I'm not going to be publishing any papers and most people who are self-taught will not either. It's not a goal of mine besides.

However I'll still take a stab at the Erdos-Sekeres conjecture of the convex n-gon from time to time. I realize someone else will solve it but what's the worst that can happen? It's fun and enjoyable and sometimes I wish there were more people who found mathematics as enjoyable as I do. And that it was more accessible.