In a round about way we're saying the same thing.
1.) He got the axe to base camp. . .how? He carried it there. Never said it had to be attached tot he hip 24/7. In my example mountain men. . .carried their axe in. Maybe on a mule or horse, but it was carried in. Didn't say they carried it 24/7. If we're going to get hung up on "carry" then say "brought with".
2.) Remember I lump hatchets in with axes. It's really not hard to carry an axe (er, hatchet).
3.) I bet he didn't use "any old pocket knife" to build a cabin, chop wood, split wood, do heavy chores like say, split a pelvis. Like I said, an axe (or other big blade for heavy duty use) was brought for heavy chores.
4.) Again, IF an appropriate heavy suty tool was brought, then the knife doesn't have to be strong at all.
5.) The ONLY time I said a knife HAS to be strong is if it's the ONLY cutting tool you're going to bring and use it for all chores. If others want to cut, buck and split firewood for the prospecting camp with a Mora or Buck 110, go for it. Not me.
Once you have the problem of heavy duty uses out of the way, the knife doesn't have to be much. A Mora, SAK, kitchen knife, or sharpened piece of sheet metal will all work provided you keep them sharp for knife chores (see the "Knifecraft" section of Mors Kochanski's Bushcraft book for knife chores).
I am sure neither of them did this with a pocket knife...mainly because I am sure neither of them did this while living in the wilderness.
I know my dad never built a cabin anywhere because he wasn't in any place long enough to warrant it, and I know my grandfather built a few houses, but they were entire houses in isolated places, and he was living there while working at a mine close by, not surviving in the woods.
And I guarantee neither of them split a pelvis while on extended trips into the woods, because they would have both been alone and wouldn't have shot anything big enough that they were unlikely to eat over the course of a few days.
I get what you are saying - an axe is a superior tool for heavy work. But my point is that in terms of surviving day to day out there, unless you are feeding a fire to stay warm in the serious cold, or chopping up ice to get to water, there are fewer heavy chores than most people would think.
I know the only situations I've needed an axe for were in long term severe weather, where I had to cut about 8" into standing deadwood to get stuff dry enough to burn.
But these are extreme conditions...most well prepared people (hopefully all of us!) would have sufficient clothing and gear to create microclimates that meant we didn't NEED to burn a cord of wood a night to stay warm, didn't NEED to light fires from whatever was around on day 50 of a rain storm, didn't NEED to supply a large camp with so much water that chopping through river ice was necessary.
Of course it's pretty possible that you would need to do all of that stuff, but to my mind that would also be pretty predictable. If I was going somewhere long term in heavy weather I would ABSOLUTELY take a tool for heavy work. If I was going somewhere temperate I think it would be less critical. And for sure, neither my dad nor my grandfather would have thought twice about it.
But I definitely get what you are saying - if it's the only cutting tool, AND you are out somewhere long term, having a lot of fires, setting up a stationary camp (dad wasn't at his base camp often enough to make it nice and his base camp moved every couple of months anyway) then I definitely agree, under those circumstances you would want an axe.
I just don't think that's very many of us here, is all.