"Have you ever handled one of these hatchets?"
Gransfors Bruks and Wetterlings are great examples of hatchets, with incredible steel and head profiles, but....
I lived with only wood heat for years and I've swung my share of sharp steel around. The problem with hatchets is that a user will have their hand in harm's way, or try to use the tool for heavier tasks than it was designed for. An inexperienced user who is tired, dehydrated, or on the edge of hypothermia (or all the above) is a poor candidate for using a hatchet. Small hatchets can bounce and ricochet in unskilled hands, especially with springy green limbs.
On the other hand, a folding saw is about 1/4 the weight, 10% of the cost and will cut small diameter wood in a hurry with little chance of the user gashing their shin open or lopping off a finger (yes, someone will still try).
If it comes to emergency shelter making, I can do it much faster with a saw. I can cut some big stuff by simply cutting from two directions. If I need to get to the dry center of a dead limb, I can cut part way through and peel it back to split it.
In the video, Ryan is splitting off small sticks for tinder. I can easily to the same with a $12, 4oz Mora knife and a stick, with my hands completely out of harm's way.