Thank you for the link and I should fix part of my post, the kelvin probes I was lookng at are Keysight/Agilent ones for 183
The biggest reasons are low sales numbers, high part count, high quality and of course the corporate name. I will compare these throughout to standard test leads to explain the costs to SOME degree.
When you compare the sales of Kelvin leads to test leads, the ratio is likely 1:1000. This means you have a MUCH smaller pool to make up your tooling and manufacturing costs. Additionally, when you compare these to a standard set of test leads, these are drastically more complex devices. A standard set of test leads is comprised of a sharp metal tip, soldered to a wire and then placed in a mold. Thermoset polymer is injected into the mold and then a formed set of test leads is born. This is a VERY simple, easy and CHEAP methodology. When combined with the economy of scale, this is why you can get quality test leads for very cheap. Klevin clips on the other hand have loads of parts, the wire loom, the heatshrink, 2x more cables minimum, etc. All of these parts cost money, not just to make but to assemble and these costs have to be spread over a much smaller number. Plus being a Keysight product they are likely made of at least acceptable quality parts. These are NOT budget basement parts. The people that need Kelvin clips in a corporate environment will have a much easier time getting Keysight branded ones than no name branded parts for a variety of reasons. So the fact they are from Keysight and not from Uni-T, GW Instek or PedroDaGr8's Backyard Basement Shop O' Fun is worth some money.
Now does all of this add up to $189, not really but that is what they thing the market will bear. Plus, the high price gives them some leverage in negotiations on instruments. They can throw in this "$189" set of leads for free! In reality it maybe cost them $20-30 in parts and assembly MAXIMUM. Frankly, in Kelvin clips you don't really need that high of quality. As several people mentioned, you can make the wire as thin as possible to carry the current without affecting your reads.