You're kind of missing the point.

Rote memorization of times tables doesn't lead to understanding. So, early in the learning process, you give children techniques that give correct answers, boost confidence and increase understanding of what is actually happening.

Thus when they see 4x = 2y they'll know that 4x means 4 xs and 2y means 2 ys.

Actually, I think that for most students they hit a wall in Algebra regardless of how they learned basic mathematical operations. This wall has to do with abstraction of principles not with mechanical operation speed.

If what we are trying to teach is this abstraction, then the rote table method is arbitrary* and a time sync. The students will still learn basic sums over time, it just won't be the focus of the practice.

*For instance, my education with the tables went up to 12s. Why in the world did we choose 12? 16 would have certainly helped me out more.

I have 0x65 problems and knowing 12*11 from memory doesn't solve any of them.

Rote solves everything and nothing. Faster time to correct answer, yet no understanding of solution. I'd rather have people who can reason and fumble through a problem than can rattle off memorized facts.