Finland tried teaching maths to children using Group Theory in the 70s [1], but the results weren't that good; it proved to be too abstract for young kids.
Ultimately, I believe basic algebra and geometry are the most important takeaways from math classes for most people.
I am no expert in pedagogy of mathematics, and I am sure someone will correct me if I am wrong, but I think there was/is a Russian academic program in which students were/are basically only taught algebra in an iteratively increasing manner.
As it was explained to me, one wouldn't take a "Calculus I" class as a prerequisite for say an entry-level engineering course. One typically had such a strong foundation of algebra, that when encountering a problem that required calculus, the student would just learn the necessary calculus at that point in time. In other words, with such a strong algebraic background, other aspects of math, within reason, were much easier to grok.
> the results weren't that good; it proved to be too abstract for young kids
You cannot make that conclusion as a result of the evidence. Yes, the evidence might support that conclusion, but there are many others that also could. For example, they could have just been really bad at teaching. This even seems like a likely one as it is difficult to perform such a reformulation and to do so broadly and quickly.
The other reason I'm willing to accept alternative conclusions is that France and the USSR had far more success than Finland (or even America). Their success contradicts a claim that "[it is] too abstract for young kids". You'd need to constrain it to something like "[it is] too abstract for Finish kids" which I think both of us would doubt such a claim.
Ultimately, I believe basic algebra and geometry are the most important takeaways from math classes for most people.
[1]: https://www.hs.fi/tiede/art-2000004823594.html (sorry, it's in Finnish and behind a paywall)