Math teaching selects for people who do their homework everyday. This is very different from what actual math selects for.
Unfortunately, this selection misses (most?) children who may not be well suited to "school maths" - for whatever reason. But these children may succeed just as well in "higher mathematics".
Two anecdotes: (1) June Huh dropped out of high school and stagnated for 6 years in university. In his 6th year, he ran into the fields medal Heisuke Hironaka. It was only then his "slow thinking" and deep creative insight (perhaps the things that hindered him in "school maths" type courses?) proved to be fruitful in higher mathematics. June Huh now has a fields medal.
(https://www.quantamagazine.org/june-huh-high-school-dropout-...)
(2) I was frequently in trouble at school and underachieved relative to my predicted grades. I resented the route learning and arbitrariness of "school mathematics". Due to some miracle I'm currently working towards a PhD in theoretical physics, in the mathematics department of a top university, and I also spend about 90% of my free time working through various advanced maths textbooks for fun. Turns out I'm quite suited for thinking about higher mathematics, despite not being particularly well disposed for school. If my school experience was different, I probably would have done a PhD in pure mathematics instead.
I somewhat disagree. There were plenty of students who start to hit higher classes and just don't have the aptitude for it. They really didn't know it wasn't their thing until junior year of undergrad, despite always being told they were "good at math" as a kid.
"Back in my day," my school district adopted a math curriculum that introduced sets in first grade, and eased us into proofs. We were not unfamiliar with proofs when we hit high school geometry, which was almost entirely proofs. Also, by doing proofs we could recognize that the manipulations we were doing in the regular problem sets could be seen as mini-proofs, rather than just guessing the right algorithm and grinding through it without knowing why.
When my kids took math, no proofs. Even geometry was all problems and no proofs. Moreover, kids are all aware of the conventional wisdom that "you just need math to get through school, you will never use it after you graduate."
For me, proofs were what made math come alive, and I started college as a math major. Today, despite my theoretical bent, I'm one of the few people at my workplace who is willing to solve practical math problems that don't have a canned solution in a software package.
I never did any homework, and that worked great until undergrad, where the strategy of reading things on my phone all day instead of listening to anything in class stopped working quite so well.
I'm not very good at proofs, but following arbitrary rules provided with no motivation? Decades of experience!