The clamp on is evidently well optimized for its intended purpose.
The thick laminations, probably silicon steel (for ruggedness and low cost) really cut the high end response with their eddy currents, and the inevitable air gap (low effective permeability) in a clamp structure chops off the low end response. A good, thin foil (low eddy current), nickel alloy, high Mu, tape wound CT core greatly improves on both ends. But they cost more than that magic $10.