Dave, I think it's simply just about what you feel like carrying on any given day for whatever reason. Neck knives have a place for sure, but certainly not for everyone or every situation. All the ones I use either have the option to put on a belt at a seconds notice or are small enough and secure enough in the sheath to just put into your pocket. I love folders with clips as well, own plenty, and carry them often depending. Talking about being active, on several occasions, I have caught clipped folders on things, branches, whatever, and had that folder pulled right outa my pocket. The ones pictured above, you'd have to do something crazy to get them to come out of that DEEP leather sheath. I'd definitely say point down like the leather sheathed models above, is the safest. Tip up would be primarily for kydex sheathed designs ..... and even if the kydex is molded tightly, I still feel better about point down, mostly for loss of the knife.
Sometimes, you just want / need a fixed blade. Little fixed blades are incredibly strong. A neck knife makes a great back up blade for a larger camp or bushcraft blade, often more capable of the finer detailed jobs that are too cumbersome with the larger blade. The right neck knife can be a great self defense tool that is concealed. You see pocket clip folders in everyones pockets these days, advertising not only that they are carrying a knife but what hand they most likely use it in. Lots to consider ...........
I'll be honest and say most of the time these days, I've taken a liking to the Leatherman multi tool. It gets a ton of use.
If you are hanging at the lake, beach or just dressed really thin because it's so darn hot out and you ain't got pockets or a belt on your swim trunks ......and you want to have a knife handy, a neck knife is a viable option.