"That process works both ways. One look at the member map will show you where the largest audience is. It's not Montana."
But they may go to Montana :)
Other than the weight, that nice Gransfors Bruks hatchet that Ryan was packing is a cool $100 or more. Elegant and shown in trained hands, but it is this really practical on a SUL diet? That hatchet is about 20% of the remaining base weight!
FYI, Vaughn makes a light hatchet that you can find for $20 or so, but I think all of these small axes are miserable tools. They bounce and slide around, and if one ricochets off your cutting target, it can make a righteous mess of your shin or lop off a finger with great ease.
For a small cook fire, there are plenty of lighter and actually more useful alternatives.
Show below:
Gerber sliding saw. 4.8oz and about $12. The blade is 6" long and cuts very quickly with light effort. A tired or inexperienced user won't do major body damage with one far from help as they might with a hatchet.
Mora Robust knife. 4.8oz and about $16. Useful enough for preparing fire wood alone, but I think it makes a perfect paring with the sliding saw. You can use this one to clean a trout or pare an apple, which would be interesting to try with the hatchet. I'm not a fan of heavy batoning with a knife (where the hatchet excels), but I would by fine splitting the small stuff shown in the video with it.
Victorinox Farmer knife. 3oz and about $32. I think this is the most elegant alternative in the pile. You get a saw, a rather thick folding blade (thicker than other 91mm models), a very good awl, and the typical SAK can opener and bottle opener. If you want tweezers and toothpick, you can get the very similar Hiker model at about the same weight and less expense. You could baton small, dry straight-grained stuff with it within reason. This knife with scissors would be incredible. I carry a 3/4oz SAK Classic to get scissors, nail file, etc.
Wenger Handyman. 3.2oz and $35-$40. Much like the Farmer above, but a few more tools— notably a nice pair of scissors, and you get tweezers and toothpick too.
Victorinox Trekker. 4.6oz and about $35. You get the larger saw, a locking blade, plus awl, bottle and can openers, tweezers and toothpick. Big on my go-to list for an all-around trail knife. The plain blade version would be better for fire building. I wish Victorinox would dump the screwdriver/bottle opener and add ***scissors***. BTW, the blade on the one hand model is much thicker than the other 111mm models.

Cutting tools aside, I do applaud the incredible simplicity of this setup: go for a nice walk in the wilderness on a summer day, throw your bivy down, have a nice little fire, cook your dinner and sleep under the stars, just the way the Creator made you. Good stuff.