"Motivation" at a higher sense is something that's sorely lacking in US public school (free government school) math. Especially prior to real algebra, the teachers tend to be generalists who don't know to tell you "you need to learn X so you can learn Y which will allow you to solve problems like Z" and of course get you to understand why Z is neat and important. But that's a different sort of problem that just not making sure all students capable have the foundation they need.
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.
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.
The book A Mathematician's Lament really registered with me due to this experience.
So, while I don't know enough about educational theory or the Common Core mathematics curriculum specifically to say for sure that it is better than rote memorization, I can say my bias makes me think nothing could be worse.
The math practices I see elementary school kids doing under Common Core seems to be way more like "real" mathematics than what I did at that age.
I will say, I worry about the population of elementary school teachers who are asked to implement this, as a generalization they are the least likely to have taken advanced mathematics in university.