The reason the adds don't count is not because they arbitrarily decided to ignore them.

Addition is O(n), multiplication is more than O(n), by the nature of the big-O notation, when you have to do a series of operation, you only have to count the ones with the highest complexity. So in the Karatsuba example where the formula involves both additions and (recursive) multiplications, the additions don't count only because the multiplications dominate.

Or, as a formula, O(n log n) + O(n) = O(n log n), and btw O(n/2*10) = O(n), in big-O, constant factors don't count