This is what is called a "positional arms race". A comparable situation can be seen in football players and steroids. One does it, so all feel they must do it or be "left behind". For all this struggle, no one is better and most are where they started. Now they must also deal with the huge medical issues that steroids can cause. If every one stopped, all would be better. However, no one wants to be the "sucker" who stops: the first to do so actually
will lose.
It's the same issue here: interesting opportunities have a limited number of slots. My benchmark for getting in is not an "A" or a "B+", it's whatever my classmates have and then some. We all study more, but are not any better for it.
There doesn't seem to be a solution that has been devised for this sort of issue in this sort of a case, as it's tremendously difficult to find any viable means of regulating how much free time a child receives (leaving aside the ethical/moral questions about such a practice).
It's not just childhood, though. Higher education [0] has experienced it. Indeed, any "positional good" which has a limited number which go to the "best" is likely already experiencing this or will soon.
Again, no one has yet found a perfect solution for such an application as this. We've tinkered with the positioning in certain cases (e.g. higher education and affirmative action), but it often doesn't work (in the instance of higher education, while all kids' childhoods may be screwed up, certain groups have theirs screwed up in the "right ways") [1].
I believe another example is the rise among millennials of "experience" vacations. Increased social media usage fuels envy and a perception of being lesser, meaning john doe now feels he needs to take a more exotic vacation and get more pictures with more retouching.
I see no easy solution to this. The normal mitigation is government regulation, but I see no "arms control" type solution for number of math problems done. Ideas, any one?
[0]: https://eric.ed.gov/?id=ED474473
[1]: https://www.theatlantic.com/national/archive/2012/10/the-pai...