I think in Asia though it's expected of highschool students to evaluate the integral without a calculator. Education in the US should at least match what they do in Asia to stay competitive.
I do agree with you that in theory we can do better than asia, but that is too high of a milestone given that we are basically currently significantly worse than Asia on all fronts.
Adopting elements of the Finnish model would probably be an improvement.
With geometry, the style I was taught emphasized explanation of complex problems using proofs but building from first principles.