An interesting thread but I find it funny how some people are trying to constrain a style of knife carry to all aspects of blade form and function. I see three main trends in use patterns coming out of this thread.
1) Every day carry (EDC) as an alternative to the pocket knife. Folks in this category want a very small, lightweight knife that can be worn under urban clothing like a collared shirt or t-shit without printing the shirt. Knife size and shape that facilitate concealment are desirable here at the expense of knife thickness and blade length. Prime examples of this seem to be the Buck Harsook and similar tiny neck knives.
2) Self defense knife. A lot of folks refer to neck knives as SD tools. In this case, knife useability takes takes some precedence over its concealement. Examples here seem to be the those with finger holes in the handle to facilitate grip to offset small handle size e.g. La Griffe neck knife comes to mine or the Spyderco swick, and skelotonized handles to minimize weight. Note I'm not trying to imply that these knives are only useful for SD as their functionalized handle does provide utility. These knives seem like to be comprimise between concealment properties, handle usability and light weight. This is probably the most common type of neck knife and I can think of other examples: buck kaala, Fehrman thruhiker, Swampwarden, rat cutlery neck knife, becker necker, Gossman PSK...
3) Neck knife as an alternative to belt knife carry. These knives are generally used for outdoor or working applications where belt carry is impractical. This may for example be due to a person sitting such as in a boat, where the virtue of sitting makes access to a belt knife inconvenient or wearing a belt sheath uncomfortable (jabbing your lovehandles

. Issues of belt knives interferring with back packs, lack of belt (e.g. snow suit) or special access needs such as fishing are often cited. In this case, the neck knife is often worn over top of clothing not underneath it and concealment is less of an issue relative to functionality. The knife can be bigger with a more functionalized handle - e.g. using scales to thicken handles somewhat. Clearly the larger size comes at an expense of comfort. As a knife gets too big, then alternatives to neck carry - such as baldrics (over shoulder/neck) come into play. You often see people citing using non-traditional neck knifes in this category. For example RAT-3 knives or others 'small' belt knives. I would even go so far is to suggest that people purchasing knives from category 2 who wrap their handles with cord wrap are actually bulking up their knife to convert them to category 3
My neck knife - I tend to subscribe to camp #3. My neck knife was actually designed as a small belt knife with thinner scales (1/8"). It is a Breeden Kat Knife, 3.25" blade and 3.75" handle. I had two custom kydex sheaths made, one for belt carry and one for neck carry. I find in the outdoors I use both modes of carry and will even pack the alternate sheath with me in case I want to switch carry modes on the same trip.