You are making some big assumptions here as to who the audience of this board is 
My ring is 100ā wide. Most of my personal friends who have their horses at home have a ring thatās either 80ā or 100ā wide, some of them bigger (jealous). Where I boarded for many years, the main ring was a good bit more than 100ā wide, and the secondary rings were at least 100ā if not more, though not as large as the main.
Many people raise youngsters at boarding facilities with nice rings, certainly 100ā or so wide.
Where I boarded my WB during his yearling year, there was a big pasture, and a 200x300ā paddock. He learned to jog in hand, and ālungeā in that paddock.
When he was a long yearling he moved to a small facility that had a medium pasture, and a smaller pasture that was about 100x250 and thatās where he learned to w/t under saddle.
Not everyone has a, or only a, Dressage-size arena
We arenāt all Dressage riders 
and Iāve never found a lunge whip that is long enough to be effective at 10m distance (the radius of the 20m circle)
Hence the shorter lunge line and walking a large circle. When teaching even an adult horse to lunge, I never let the line out so much that I canāt reach them with the whip while the learning to go is being established at the walk and trot, and since Iām still able to move fast enough, even at the canter.
so, especially when teaching a horse how to lunge, most people keep the horse within reaching distance of the whip, not to strike them with it but to be able to use it as a touch if the baby needs encouragement to keep up forward motion.
I fully agree, and thought that was made clear a few posts ago about walking a large circle with the youngster, but maybe the closeness of the handler was not made clear
Also if you are going to lunge a horse you should keep yourself fixed in its centre, some texts recommend pivoting on a heel, so that the circle is circular which is not the case if you walk a circle within the circle. Having a circular circle is important as it allows the horse to know where they are supposed to go and so keep their balance and avoid too many corrections from the handler if they deviate from the desired path which can happen if the circle is more like an oval or an octagon.
When lunging for training/exercise, I fully agree in most cases (there are always exceptions and Iāve been in a few). But for this purpose, I donāt at all feel itās necessary to keep feet planted so there is a very defined length of line, as thatās not the point for this purpose.
Edited to add Iām saying 15 metres which is similar to 15 yards. Not 15 feet. Youād (hopefully) never dream of riding a very young horse on a 15 metre circle as its just too small for their balance. IMO the same is true for even younger horses and lungeing.
Yes, I know what 15m is
Iād never work a yearling on that small of a circle
Not even a green 2yo or 3yo or any green horse regardless of age, though you could progress to some gait at that diameter sooner with the older horse