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.