My example used ints, but I was being deliberately vague when I said "bignums". Balanced-tree reduction certainly isn't optimal for ints, and may not be optimal for anything, but it's pretty good for a lot of things. It's the comparison-based sorting of reduction algorithms.

* When the inputs are of similar sizes, it tends to produce intermediate operands of similar sizes, which helps with Karatsuba multiplication (as you said).

* When the inputs are of different sizes, it limits the "damage" any one of them can do, since they only participate in log2(n) operations each.

* It doesn't look at the values, so it works with third-party types that are unknown to the stdlib.

There's always a fallback case, and balanced reduction is good for that. If there's a faster path for ints that looks at their bit lengths, great.