When we homeschooled the kids, they didn't get calculators. They learned long division too. Never could get my daughter to memorize multiplication tables though and I only asked for up to 10 x 10. I know them up to 12 x 12 because I'm blue collar and use inches/feet and knowing how many inches are in 1 - 12 feet is handy. I also know my decimal equivalents by heart down to the 16th of an inch and can figure out/remember the 32nds from there.
Daughter always kept one of these handy.

I had her make the table but with 0 in the bottom left corner, AutoCAD style. Tried flash cards and was hoping having her make and reference the table would help her remember but she refused. It was a rebellious thing. Because she knew I wanted her to learn it, she refused. Didn't matter if it was for her own good.
Aaaahhh......... the popsicle stick matrix. Mrs King would be proud of you
When I was in fourth grade, we did the popsicle matrix a lot. Each of us was required to have a pencil, some paper and a popsicle stick
It turns out that a popsicle stick used as a guide produces horizontal and vertical lines that lay out a square matrix. The first and left rows are filled in with the digits 1-9. The other blanks are filled in with the multiplied number.
It has been a while but as I recall, the popsicle stick produced a 10 x 10 matrix square and thus allowed multiples up to only 9 rather than the 10 in your graphic.
Multiplication table to memorize?? Your raycizm is showing!
We had to make those in elementary school. I don’t remember what the minimum was, but you could take it as far as you wanted. And if I see “169,” I think 13 squared. And doing 17x19=100+70+90+63 is second nature. The brain needs to be trained.