I've always thought one of the most important goals of learning math was learning how to think logically. This may be coming from a physics perspective where the language is used because it is (arguable)the most accurate tool we have to analyze the world around us.
The average person doesn't need efficient proofs and algorithms. But they can use generalized facts.
I think that the idea that studying math is necessary to train one's logical abilities is a misconception. Learning any of the sort of non-trivial activities, such as cooking, which requires a high degree of awareness and logical thinking, would have the same side effect.
Sorry if it came off like that. I don't think it is necessary, but it sure is a helpful tool. So if we're going to teach people basic math skills we might as well focus more on this aspect so that they can use those basic skills and know why knowing how to find the angle of a triangle can be useful.
The average person doesn't need efficient proofs and algorithms. But they can use generalized facts.