Your concerns are well founded. Any blade more than a cross (+) shape will mean that the wood has to be compressed between two blades. If the blades are held parallel to each other and can float, possibly they would work okay.
For sure, the wood won't compress (like the potato will) and something will have to give. A friend built a multiple blade firewood splitter, and while it was a good adventure, it didn't work. He had a huge hyd. cylinder from a garbage truck and a 6cyl power plant, with a huge pump, but couldn't build the splitter blades strong enough to compress wood. If light-weight wood was split (like aspen or cottonwood), it would come out 'smushed' and extruded-like. For oak or elm, the wood became stuck in the blades.
The forces to compress wood are high, and the splitter would have to be super thin blades and super tough.
In short, I doubt it will work for wood, like it will work for potato's.