The core, being in the middle of the laminate, is subjected to almost pure shear forces particularly at the neutral axis. I completely agree that if you have pure shear loading in the end grain direction this leads to tension/compression at 45 degrees to the grain (stress transformation).
However the original question was, Is there a reason not to run the grain parallel to the CF? The answer is yes. The higher compression strength is needed in the directions the loads will be applied which is typically to the top or bottom of the beam.
For a splitter you could probably get away with long grain balsa if you are not going to bolt through the core. However, I don’t think you will see much benefit in bending since the modulus values for the carbon or glass fibers in the skins are much, much higher.