Forgive me if I've missed it -- but I didn't see any mention on the physics of splitting wood (e.g., along the grain).
A splitting axe only has to initiate separation of the wood fibers. Then the shape of the cheeks and kinetic energy of the axe head ensures the initial separation of fibers propagates into a full split. Theoretically, the fibers are not severed. They are separated like peeling apart a piece of string cheese.
A knife, with its keener edge, is more likely to sever the wood fibers at obtuse angles as it travels the length of the log. What this means to the user is higher friction between the blade and wood, which translates into more effort required to perform the same amount of work.
Obviously, that is a simplistic view, as some effort is still required to hoist the splitting axe (or the knife baton), and the size of the splitting axe has to be suitable to the size of wood being split. For smaller splitting jobs the knife could be superior.
If I'm on the trail and only have space for one blade, I carry an 18" Wetterligns splitter! It's thin and keen enough to cut and chop, but still has cheeks suitable for splitting. It's my general-purpose axe! My personal preference when I can't avoid the compromise of carrying only one tool.