Of note - the canon version is that murder rends the soul, and a horcrux merely preserves one part of it in a separate object than your body. Dumbledore did not need to create a horcrux to have sacrificed the contiguousness of his soul, assuming canonical soulphysics at least.

Of course, I see no reason not to create a horcrux if you're doing murder anyways(unless there are significant additional costs associated), but then Dumbledore has a very different view of death than I do.