Cleaving is mostly about friction. Cutting a block of cheddar is pretty much all cleaving, and a very sharp cutting edge doesn’t provide much advantage. My blade vibrates along the blade face, so foods experience the coefficient of kinetic friction, not static friction. This reduces cutting forces, and does so in a way that’s totally independent of the sharpness of the edge.

Looks like the inventor posted a comment explicitly about cheddar in the link.