Why do schools still teach arithmetic algorithms?

I think that's it's really cool to learn the algorithms, as tools that improve reasoning in math, in CS and in systems thinking in general.

What I dislike is the focus on avoiding errors. I think it's beyond silly these days to deduct points from a student when they got a couple of questions on a set wrong, but clearly understand the algorithm. We should figure out a way to teach algorithms without focusing on manual execution of them. For older kids, the proper way is possibly to get them to implement them in code, until they pass the given test cases, and for younger kids, I suppose that despite its costs, I'd go back to oral examination.

I do plenty in my head and some by hand.