A puukko is not an ideal all around use style of knife, which is pretty much what you described. A properly designed blade with a finger choil can eliminate the requirement to carry a small knife for detailed work and a large knife for more coarse work. A simple change in hand position allows you to instantly go from power chop strokes to fine small amounts of material removal. Like chopping a stick to make a stake, then using more fine movements to refine it. Same goes for notches.
A properly designed choil will save time and is more safe than having to keep changing knives or have two out at the same time.
I can see the confusion though if someone thinks they will do power strokes to chop a branch to length for a stake using the choil, then choking down and not using it for the finer carving duties.
The pinch grip, even with a puukko isn't going to remove dense hard material anyway. You will still need to wrap your fingers around the handle to put some power behind it. It won't take but a few slices of dense hard material with a pinch grip before someone changes their grip. Like I said before though, it works great in the kitchen. Other than that I don't see a reason for it. It's probably the same reason you do not see a choil on a kitchen knife. The pinch grip works perfect on a kitchen knife, it's not needed in there.
More than just Puukkos have edges ground up close to handle. Also, James isn't talking about using the pinch grip for "hard roughing out of material". That's what the real handle is for, because it offers a full grip.
The pinch grip is to get great control of the tip for delicate work (fine carving where the chord of the knife is too wide to get where it needs to go, removing splinters, cleaning under fingernails, etc). Using your offhand to help control the tip (use the thumb), or using a pinch grip puts you directly over the tip. If you use a choil on a 5in knife, your finger/hand is still a minimum of ~4in from the tip. And the difference gets larger if you change that to a 8-10in blade where you are still at least 7-9in from the tip.
The argument for a choil seems to make more sense for a larger knife, where it helps change the balance point to something more manageable for close up work. But, alternatively, you can just use the knife differently for fine tasks just as easily. You can swing the knife into a stump edge, then use the now fixed position knife (as its stuck into the stump), and move the material instead of the knife (similar to the knee lever grip/cut, but with the blade supported by the stump), just as a "for instance".
Additionally for the size knife the OP (and presumably yourself) are talking about, lacks the ability to chop to chop well (4-5in blade). Using "power chops" aren't going to work well, and what ends up happening in a knife this size is that its longer in OAL than needed without doing either task particularly well.
The irony is that a knife with a choil needs a choil MORE, because the edge is so far away from the handle. So I can see how using the normal handle position might feel a bit useless for fine work on a knife with a choil.
Anyway, like I said before. Its a personal preference thing. I just feel they don't make much sense for most types of blades, so I avoid them on my knives.