So, if we take the left hand side of the illustration showing the left and right handed version of the "so-called" correct grip, that is, outside hand nearest the axe head, it's plane that this takes a reach across the body causing a dip in the shoulders and a twist at the hips, or the effort required to overcome these natural tendencies. In the other case when the inside hand is the one up high and the outside hand down low there is no unnaturally twisted posture as a result. Both hips and shoulder are comfortably held in a 90 degree relation to the axis of the stem, (see photo above).
Notice how the body faces inward toward the face of the timber as the hewer reaches across his body to grip the axe up high with his outside hand. (I pinched this picture off the internet just to illustrate a point.)
Why is that handle on the broadaxe bent like that? Mostly you will get the answer that this provides for space between the knuckles and the face of the hewn surface, it seems apparent but is it. What if the sweep has nothing to do with the hands but instead is meant to keep the shoulders in this squared up relationship by bringing the rear outside hand in line with the shoulders squared to the face of the timber? Isn't that the more natural position? Doesn't that give a better reference to the result we are after? That the instrument is like that to facilitate the results directly and not indirectly by making the user feel comfortable in a way that gets the hands out of the way literally and figuratively?
It is the hand out front that does the lifting. In the case where that hand is the one next to the timber the forces are only vertical but when the outside hand is gripping up there a correction has to be made to make up for the off-centerer position of the source of the lifting.
I have to wonder if all this makes any difference because it's obvious that the log's get squared up regardless. In one way, maybe is comes down to the effort expended to get it done and working in an efficient way, that way which will be least demanding physically and mentally so that the process becomes sustainable in the long run. I mean in the end it is all about energy, from my perspective. If I get the idea to square up my own timbers but after one timber or one project I find that it is just to much work and not worth it, probably that will be the end of it and I will just have the story of how I squared up those logs that one time with an axe. But if the work goes well and the results are good then it becomes an alternative to the other options available, then I have achieved some degree of choice and become that much more independent instead of just clowning around.
That's my side of it and it would be better to have some countering arguments no, lets say alternative visions.