I think you're on to something in your bottom diagram: A little neck popper that will go either way!
The bottom picture is the normal way you would go to turn anything. The ends would have to be trimmed. So you would end up with a plug that's less than the length of the piece you started with. I don't use a plug that's much over 8 inches, with the most common being 3 to 6 inches.
I imagine that the piece could be turned right down to the very end of the stick, as in your first diagram. But in this case, you're always going to have to deal with the marks left in the ends of the stock from the gripping device centers on both ends.
If you're through-wiring your plugs, you'll need a hole down through the center of it. Making that hole, either in the unturned stick or in the turned plug, is somewhat of a challenge because it's hard end-drilling on a drill press, and getting it in the middle all the way to the end. So I want a lathe with a bored tail stock so I can run the bit through it while it's spinning on the lathe. Some combination of centrifugal and centripedal (sp?) force helps (no guarantee) the bit find and stay in the center, if you're using a bit that is stiff enough.
Lastly, I think the advantage of a long distance between centers on a lathe is that one could turn six or eight plugs, or more, on one stick, say, three feet long. Then cut them off and go about finishing them. But, depending on the kind of wood the stick is made out of, increased length introduces the risk of the stick "exploding" while you're turning it. This would produce about a million toothpicks of assorted sizes, some of which are sticking into the operator. These things only spin at speeds less than 5000 rpm, from what I've seen. Industrial wood lathes spin up around 15,000 to 20,000 rpm where "exploding wood" is a real danger, expecially for maple, birch, and long-grained woods like oak. I like maple plugs--very hard and dense. Others like cedar or pine, very soft and un-dense.
Just my thoughts.
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