That's the most important thing involved, having the other end of the bore centered accomplishes nothing except having both ends of the barrel centered on the AXIS, which is nothing but an imaginary line running from the center on one end to the center on the other end. But that's what you WANT is what some will argue! But why? That axis is not representative of the bore and is just an imaginary perfectly straight line extending through the barrel with the bore wandering around it along it's path from one end to the other. I think this is the flaw to the thinking when centering both ends, confusing that AXIS line with the actual bore but it's the bore that matters! Nothing we can do is going to align a less than perfectly straight bore along it's full length but we can align the last few inches of the bore so that the cartridge is in alignment with the BORE, to heck with the AXIS because that bullet is going to follow the bore not the axis! By centering both ends of the barrel we align the cartridge/chamber with that axis and because the bore will almost certainly be wobbling by some amount at that point due to the fact it does not truly follow the axis then we end up cutting our chamber true to the AXIS but at an angle relative to the BORE. By allowing the outboard end of the barrel to locate at a point regardless of center that will have the indicator rod indicating true along it's entire length we will have centered and aligned the last few inches of the bore, if we then cut a chamber it will not only be centered but in alignment with the bore itself.
I fail to see how those who insist both ends MUST be centered can't see the problem? If we had a visible curve in the barrel it would be easy to understand, when centered on both ends the barrel would be visibly wobbling around those centered ends. With our lathe tooling square with the turning axis look what a chamber or crown would look like if cut into that wobbling barrel! It's the same thing with a normal barrel just on a much smaller scale, the error is still there but reduced to a point where we can normally get away with just ignoring it. But why do that if we can avoid that tiny error altogether and get an even more accurate cut? By allowing the outboard end to go to whatever point off center it needs to in order to get the indicator rod to run true along it's entire length then the bore is in alignment with the axis at that point on the barrel, and thus the lathe tooling also, sure the other end is off but so what? What is important is that the chamber/cartridge be pointing parallel to the bore at the point where it is located, that won't happen if both ends are simply centered so that the axis is aligned and the bore (which does not truly follow the axis) is allowed to wobble at that point which a wobbling indicator rod will surely indicate!