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.

Use wire.

Nah, I'm not gonna be convinced till that thing can slice through an Angel's AT Field.

Serrated knives work better on cheese, unless you need a cleaner cut, then use a wire cheese cutter.

A single bevel serrated knife will leave pretty clean cut though. I use one of these: https://www.williams-sonoma.com/products/wusthof-gourmet-serrated-utility-knife/

Even works pretty well on softer Monterey Jack and pepper jack (which the wire snags on). And I’ve never sharpened it in 20 years.

But paid less than half that at resellers store.