I have carried pocketknives most of my life. Never had one with a half-stop till a couple of years ago when I started to "get into" the hobby, if you will. Maybe it's just a preference. I like anchovies on my pizza but my wife does not. She likes mushrooms, but I loathe them.
Maybe they seem too abrupt for me. I like a knife that opens in a smooth action without jerking to a stop halfway through. I like the actions on my Case non- halfstop knives, but probably my favorite action is on my Laguiole knife from France. It opens easily and snaps open firmly, almost like a locking knife. To close I have to exert some pressure but the blade stops when it is almost half closed; then I push it slowly closed. I can let it snap closed because it has a blade stop, but I generally use two hands to close it carefully. I like that when it stops when I am closing it, it does not do so abruptly, like my Case knives and my GEC knives. It just slows down gradually. Maybe you have to experience it.
I also like friction folders like Opinel. No backspring-- you just pull the blade open, and close when you are done. No snapping closed. Also I have a Spanish navaja with no backspring. Just pinch it open and it locks with a wonderful mechanism. Closes real easy too.
Anyway, the bottom line is that I guess it's just a personal preference. I am still learning what I like and don't like.