The problem is that current (US) math education...
Worth noting that the US tried the kind of math education you are suggesting (called the New Math initiative) and it failed miserably. The math education we are seeing today is largely born out of a counter reaction to that failure.
The New Math was something fairly different than what I am suggesting. It was an attempt at an alternate curriculum for primary/secondary school based on higher-level / more abstract mathematical topics, partially displacing study of arithmetic.
The New Math curriculum per se wasn’t so terrible, though it certainly had flaws (like anything invented from scratch out of context and not slowly developed and tweaked over time in response to feedback in a real-world setting). The bigger problem was that the proponents of the New Math didn’t have much buy-in from students, parents, teachers, school administrators, or the broader society, didn’t really do any outreach or teacher training, didn’t really produce enough supporting materials, and just dumped the curriculum on schools without support.
Parents and teachers didn’t know what to make of the curriculum (were unqualified to teach with or assess it), and didn’t feel involved in the process, and as a result there was a lot of opposition.
But what I’m talking about is not teaching different subjects per se, but teaching whatever subject in a different way, focused more on solving problems and thinking than on precisely mimicking teacher’s demonstrations or memorizing formulas. The current typical math pedagogy is patronizing, emphasizes memorization/recall and very careful attention to details (sometimes irrelevant details about formatting), teaches students that they shouldn’t try to think for themselves and teaches them to conflate getting the right answer with being “smart” or “good at math” and that anyone who makes a mistake or doesn’t know how to get the answer is “stupid” or inherently incapable.
I'm not in the US, but both of those seem to be greatly focused on the curriculum. OP is instead talking about the style of teaching and learning, which could be applied to practically any curriculum.
Worth noting that the US tried the kind of math education you are suggesting (called the New Math initiative) and it failed miserably. The math education we are seeing today is largely born out of a counter reaction to that failure.