This is, actually, all true. Students should indulge in problem solving, analysis, investigation, early proof, ideas of proof, argument, explanation, and all the things that math is really about, and which make math useful.
After all, who except for science and engineering students ever differentiate a polynomial? Knowning qualitatively and intuitively what rate-of-change really means is useful. Differentiating x.sin(x) isn't.
But here's the problem.
To within 20% or so life expectency in the UK is about 70, and there are about 70 million people, so roughly at every age point (up to about 50) there are about a million people.
How do you assess and grade the mathematical standard (whatever that means) of about a million children?
How do you persuade a government full of lawyers and classics graduates that what you're doing is better?
How do you assess the teaching, and the school, if not by the grades they and their students achieve.
It's all about assessment.
So that's the first stumbling block.
The second is the question of getting teachers who are up to the task of teaching in an open and interactive manner, rather than trying to teach rote algorithms and manipulations.
But you don't need to worry about that - schools will never teach proper mathematics. They'll continue to teach arithmetic and manipluation.