I disagree.
I memorized the “times” tables and somewhere down the line I figured out what they meant and how they worked...all on my own....prolly when we started to do actual arithmetic problems.
At least that’s the way I remember it, but the 70+ years since may have provided a lot of clouds. ☺
It is likely that you used the times tables and internalized them. But it was repeated use that allowed you to retain them. I maintain that we learn best by solving problems, and learn very little by rote.