Don, availability is a huge factor. In all times past, people used certain things solely for the reason that that is what was available to them. If I could trade them off for locally available smaller white oak I would. But there is just one problem, there is no locally available small diameter white oak. In this county at least, it is almost non existent. Most of its suitable habitat has been cleared for farming, with only a few stands of ancient oak remaining. It's not all grim though, what we lack in white oak is more than made up for in spectacular black walnut and black cherry.
I have done a lot of figuring into how to best use these trees, and each length of log will yield multiple finished timbers. In some cases a single 9 foot section treated carefully may yield as many as 12 separate timbers. In order to accomplish this, after quartering (and in a few cases only halving) the logs dimensioned sections will be cut out of them. These sections will be slightly larger than the finished timbers, and will require cleaning up with the broadaxe. These will all, of course, closely follow the grain of the trees and as such will not be perfectly straight. The will be scribe fitted to each other.
This method isn't something I am just making up as I go along, it is similar to how things were sometimes done in parts of Germany for perhaps over 1000 years, maybe even more. Up until the point where German forests became man-made by virtue of continuous harvest and replanting.
Small dimensioned timbers can be made from small trees, but they can also quite effectively be cut (with an axe) out of much larger trees, which can often times be the most effective way to utilize such trees with surprisingly little waste.
Let's go back to the cabin I posted pictures of. If you look closely you will notice those timbers are all boxed heart, but are only perhaps 6 or 8 inches wide. I find it highly unlikely that all of that wood was just hewn off and wasted. While it is apparent that no saws were used to convert the timbers, it is likely that the 'waste' was split out to be used for other things, an immediately apparent use being the roof of this very building. Such is entirely possible, and was done in the past.
I won't look for it now, but if you try you can find videos online of old world craftsmen cutting boards -not quartered boards- out of a log with nothing but an axe.
DLB