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.
That's a tautology. Memorization of some facts is useful. It's probably best when the memorization happens as a side effect of the knowledge being used frequently.
Let's invert that and close the loop: memorization is by nature a side-effect of accessing knowledge for some useful purpose. Accessing knowledge for no purpose but to memorize it is, by that definition, pointless.
A lot of memorization that people feel is pointless actually isn't. I was drilled to death on my times tables, and it's served me well in my later math endeavors, even though I wasn't too thrilled about it at the time.
On the other hand, memorizing stuff about how god created the earth in a week about 5,000 years ago was crap I had to scoop out of my brain later on.