I think this is a very astute observation. I know a lot of people who develop problem solving skills later in life after realizing that their mathematics education in high school was woefully inadequate. I don't know anyone who memorized a multiplication table by choice, and I know several professional mathematicians/engineers who haven't memorized their 10x10 or 12x12 multiplication table.

Once people see what they need out of mathematics for success in life, they never choose to memorize multiplication tables. But they do often learn new problem solving techniques.

That should tell us something about which is more important.

(But of course, we don't have to choose between the two either.)