I think he did say and meant "since the widespread advent of steel": This would not include much of pre-19th century times, or any primitive stone-age tribe useage...
The fact that most people living very close to nature today -mostly in tropical regions-, all use large thin steel blades, with great creativity to accomplish small delicate tasks (instead of resorting to small knives), kind of supports his point... They are still big blades, even if thin machetes, parang and bolos are not the most suitable for northern woods, and so up in northern climes thicker blades or axes were preferred. When the Bowie knife craze came about, in the very early 19th century -Jim Bowie dying in 1836- apparently the Bowie Knife vogue was so intense that a journalist noted "every available scrap of steel seems to be converted into a bowie knife". The "fad" lasted the entire century, until the very end of "taming" the West... I've seen 19th century American bowies made of 1/2" stock, in case you think they were all thin kitchen-type knives, and what was amazing is that it was not decorated to be a wall hanger... Many big knives of course were of a much more modest 1/8" stock in those days, but not all of them by far, and 1/8" can still make a fairly heavy-duty chopping knife... That they were typically used as weapons/intimidation when axes where available is likely, and the generally thinner stock does indicate chopping large heavy wood was not often seen as a suitable task for knives, even large ones... Today we go out on foot in the woods, mostly for diversion, and not on horses for livelihood, and quite frankly, despite owning a Gerber Hatchet with a thermoplastic handle, rather than walk with that I'd rather stay home...
It is true that today with tents we don't have to mow down trees for shelter when camping, so big knives are more of an "insurance" for when we don't have a tent, in case something unexpected happens and we are not prepared, a yet still have a large knife: It's the whole idea of a Survival Knife...
Just this past Winter, in early March when a mild day made me think I could bike way, way out, having my "biggish" Randall Model 14 with me has proved invaluable to me to break into a shed after my bike broke down, and the windchill rose to -20° C... I probably wouldn't have died mind you, but I had lots of things to do that week, and what the knife did for me that night is something I truly will never forget (at the cost of two very small chips and a few slight edge bends, and a lot of scratches I hope Razoredgeknives will buff out)... It's not exactly chopping wood I'll admit, but I did have a small saw with me, and without the knife to carve a hole and then pry out that first very thick, tough plank out, any saw would have been utterly useless, as would have the poor leverage of a small knife...
The point is that of course a small knife is sufficient for almost all uses, but you don't always know in advance what the uses will be, so aside from looking silly, a few extra inches of blade/ounces is a small price to pay for this kind of insurance. After this Winter I don't mind looking silly anymore...
Gaston