One thing I always find interesting is to see what the name of items were in the original Japanese. In the case of the DNA Splicers, it was "gene wedge." Now, this is interesting because it seems to introduce the concept of simply merging the DNA, but not in a permanent way. It's a wedge; it can be removed. Combine this with the fact that Kyurem can be returned to normal, my guess is this:
The DNA Splicers were designed to allow one creature to merge with another on a genetic level. The thing is, Kyurem and a Reshiram and Zekrom were once one creature, essentially turned into unique versions of the original dragon, personified by their aspects. Zekrom is ideals, passion and energy, while Reshiram is truth, humility and acceptance. That leaves Kyurem an empty shell: cold, desolate, constantly seeking the passion and energy which were torn from it.
The DNA Splicers therefore allow the two energetic creatures (Fire and Lightning) to merge back into itself. However, note that it retains its Dragon/Ice typing; the energy and passion never really fills the void left.
On a conceptual level, think about what the three pokemon seem to represent. Zekrom is ideals, it is lightning, chaotic and energetic, running down the path of least resistance. Reshiram is truth, it is fire, powerful and all consuming, but still warm and inviting. Kyurem is neither, it is ice, empty and incomplete, a corpse slowly freezing over. Even in its alternate forms, Kyurem retains its Ice typing; neither Reshiram or Zekrom alone can fill its void.
On another level, remember that ice is technically a crystal. Crystal reflect and distort, but they all depend on the cut. Kyurem can be filled with Reshiram or Zekrom, but the DNA Splicer is insufficient to truly fuse the three back into one; at best it allows Kyurem to act as a lens for the other two.
One thing that always seems to be forgotten in pokemon is that the pokemon world is not a strictly material world; it has a metaphysical aspect which is never fully explained. There are faeries that can "wish" someone healed, creatures which fundamentally alter the nature of reality around it, and power held within otherwise animalistic creatures that really should not be there. Its this combination of technology and fantasy that I find so alluring about pokemon.