I think you might be right and I was wrong, or at least didn't put it correctly.
Compound interest should be taught in terms of examples people will likely use. So when they first get a credit card offer at a certain %APR, or a chance to invest, they immediately pull out law of 72 and do some quick estimath.
I can't speak for anyone else, but in my case at least, that's how it was taught. I remember the teacher going through problems on the chalkboard - "you want that brand new stereo for 150$ (This was the nineties) and you decide to put it on your credit card and then make the minimum payments. What's that stereo actually going to cost you?"
Compound interest should be taught in terms of examples people will likely use. So when they first get a credit card offer at a certain %APR, or a chance to invest, they immediately pull out law of 72 and do some quick estimath.