In elementary school my son would not memorize addition and multiplication and just use strategies like this.

That became a problem later on as we just can handle a finite number of intermediary results in our brain, so just memorizing the tables reduces a lot of mental load for calculation in your brain.

Another thing that helped him a lot was just writing down intermediaries on a piece of paper.

Btw it was a bit similar for me, I just got the table memorized perfectly and got faster doing simple calculations in my mind than using a calculator when I was training the multiplication and addition tables with my son.

three of the six falls into the gap between the 7 and 10, leaving 3 sticking out the top = 13.

I have no idea if this is normal or not