“My concrete has a high compressive strength. That means I don’t need reinforcing to protect against, right?”
Not necessarily, and not in all circumstances. All concrete, regardless of the mix design or the magnitude of the compressive strength, is much weaker in tension than in compression. And cracks are caused by tensile failures of the concrete.
The tensile strength of concrete is often only about 10% that of the compressive strength, but this is a rough average. Tensile strength is highly variable, difficult to predict, and is dependent not only on the ingredients and their proportions, but on the casting technique, the curing history, the amount, size and distribution of voids and defects (microcracks), etc. Even the amount of pigment or other admixtures can significantly reduce the tensile strength of the concrete.
Unreinforced countertops rely completely on the tensile strength of the concrete itself to hold everything together. Since it is already known that the tensile strength is variable and difficult to predict, relying solely on it is tantamount to gambling with a finished piece.
Often experimenters will initially try out small pieces with success, because small pieces don’t develop large tensile stresses when handled. However, success leads to bolder ventures, and longer slabs result. Eventually the sheer weight and size of the slab generate tensile stresses that overcome the concrete. Because there is no reinforcement to resist the tensile load after the concrete cracks, the slab suddenly fails and snaps in half with little or no warning.
Reinforcing steel adds ductility, the ability for a material to absorb deflection and overloading without falling apart. Unreinforced concrete fails in a brittle fashion. That is, it fails suddenly and without warning; one moment it’s fine, the next it’s broken. Don’t take these kinds of risks with your concrete countertops.