I learned the multiplication tables by memorization. Would I have been better served by having numbers explained to me, and then a guided, self-learning experience where I figured out the theory of multiplication myself?
You get utility from knowing your times tables proportionally to how often you use them. The difference between the amount of time and energy it took you to memorize them deliberately and the amount of time you would spend manually multiplying until you learned them organically defines whether or not that was a useful thing for you to do.
I did in fact learn the times table by keeping a printed one handy as I did my school's arithmetic problems -- 'cheating'. We were supposed to memorize it beforehand but I thought that was silly. My memorizing-along-the-way worked fine.
In many public schools, "oh you'll have a calculator for that!" is the common response. You don't need to memorize them, so many kids won't. But if you want to be good at foiling later on, you need to know them in your head automatically. Refusing to require some degree of memorization is setting kids up for flunking out of math later, and most tickets out of poverty these days require a college degree with heavy math coursework.
I never memorized the tables, I either had a calculator, or on the SAT and GRE or other times I don't have a calculator and need to multiply, I just draw dots and then count them up.