They don't have to "work" as in "be an efficient pen and paper algorithm", because the far more efficient algorithms is "use a computer"! They have to be good to build understanding and intuition, and e.g. presenting subtraction as "distance on the real line" is an excellent way to do this.
I did not expect this short-sighted way to look at maths education here in this website.
I did not expect this short-sighted way to look at maths education here in this website.