I guess my experience falls into three catagories; backpacking, hiking and car camping/crapping around in the woods.
I don't generally use open fire as a primary heat or cooking source when backpacking. It tends to be too heavy and impactful. Also don't generally use it when I'm camping in conjunction with another activity, like climbing. In all these cases I use a stove.
I do really enjoy building fires though, so that comes into play with hiking and car camping-type activities. A saw is the way to go for cutting rounds, IMO. If I were splitting large rounds, I'd probably use a wedge, but I don't do that when camping - I just like to make a smaller fire. For this purpose, battoning with a knife works fine. I also happen to enjoy using a knife more than an axe, so of course that is part of the picture. Enjoyment is the whole point of the trip - it's not a lumber manufacturing operation.
As far as the "bushcraft" thing goes, I haven't really done that sort of activity since Scouts (in the '70s). We tended toward hatchets and axes back then, but that was largely a matter of tradition, I think. There are definitely tasks of this sort that a large knife works better for than a small axe does (like using the blade as a drawknife, as opposed to an adz).
So... I'm certainly no big bushcraft guru, but I think the knife/hatchet thing is largely a matter of choice. A large knife is certainly not a good production tool for splitting larger rounds, but neither is a hatchet - you need a 3/4 axe for that; and then a wedge for larger stuff. What I find myself doing on camping trips is splitting kindling from, say 2" or 3" rounds. That seems to me to be more efficient/safer/more fun with a knife than with a hatchet. It can even be done with a pretty (relatively) small knife, like my BAIII. I enjoy splitting stuff that's a little larger with my FSH. Limbing small/medium branches seems to work fine with either a FSH-ish knife or a hatchet. Chopping through limbs is definitely easier with a hatchet and easier still with a 3/4, but neither compares to a saw.
If I were going to hang out by the campfire and reduce a 4"x15' branch to nice nicely sorted piles of fuel, using only one tool, my choice would be a knife. Partly out of efficiency, and largely out of pleasure.
Just thoughts.
