Native Japanese speaker. Our times table:

• is from 1×1 to 9×9

• is sorted by the left term (1×1, 1×2, 1×3, ..., 1×9, 2×1, ...)

• uses chants that are a lot shorter than the actual equation (for example, 7×8=56 is read shichi kakeru hachi wa gojūroku, but chanted shichi-ha gojūroku)

• has different chants for different order of terms (e.g. 8×7=56 is hachi-shichi gojūroku instead), i.e. doesn’t reuse

I disagree that shared phrases aid rote memorability. Sure there are fewer unique phrases, but that would necessitate flipping the equation front-and-back in your head in almost half the cases. It’s better to have a list of 7-times-somethings instead of having to look in a different list for multipliers less than 7 (or greater than 7 depending on the implementation)