I basically get and agree with your point, but I can't help thinking that there isn't some truth to this.
I think what has to change is the belief that to get this kind of benefit from math is that you have to go through the formal traditional training in it, and I have personally found that isn't so. There is a lot to do in math (beyond typical applied mathematics) that most people with average intelligence could take on and master.
No, one can not become Einstein or Hawking if they just "try". But there still may be benefits for most.