Uses of kohaishu vs santoku
Figured I'd gather all the above into an actual answer.

First, the Kohaishu. It seems this is a marketing name made by QVC for their own creation for their store brand. It is in fact a registered trademark. That compounded with the fact there doesn't seem to be any reference to that type of knife on any of the major knife makers websites, or even wikipedia, suggests it is a one-off. It seems they came up with their own design and gave it a fancy Japanese sounding name. Curious if any Japanese speakers can tell us if the name has any meaning...

As for the actual knife, standard kitchen knives range in shapes and sizes. What we're concerned here is the curvature of the blade, as that seems to be the primary distinguishing feature. The extreme curvature isn't common, but I believe that is for a good reason. With a standard one handed blade, to use the curve, you are generally lowering and raising the heel in a rocking motion. With this knife you are doing that quite a bit to use the full curvature. The main curve is also right at the tip too, which isn't where you're going to be doing most of your "mincing" motion. Generally the tip would be used as an anchor point and this blade essentially doesn't have one. All this makes it seem fairly unnatural and for someone like me with a bit of RSI in my wrist, it sounds somewhat painful. Some rocking is okay, but if you really want a specialized mincing blade, the mezzaluna seems like a better tool.

My local Japanese knife store has a great description of the standard Japanese kitchen knives (both western influenced and more traditional). You'll notice none of them have a curve quite that extreme. Having been in and had a fairly thorough lesson on the various types of blades and the techniques behind them, I can't imagine a scenario where that extreme curve at the tip will be of any use. The Santoku on the other hand, while it still has enough of a curve to allow for mincing, rocking back and forth the same way, while still being straight enough throughout to allow for slicing and dicing and does have a good place.

In short, it is a one off invention. It might be usable, but probably not ideal. With good reason I believe, the design (or similar) isn't found in any of the major knife makers inventories.