I believe a lot of it has to do with, not so much that it is round (remember Clause 9 also encompasses box tube), but that tubing presents differences in relation to groove welds and the joint configuration limitations/requirements of such.
We do a lot of box tubing welds here, the biggest issue that I see in the different approaches is that to do a CJP weld in tubing, you have to use a backer, or be qualified in open root CJPs. As for solid round bar, I can prepare a bevel in such a way that it would mimic a groove weld in thick plate, as well as backgouge it and not have to weld in a circle. Can't backgouge with tubing, box or round, normally .
As to you're example of a 4" solid round with a 1/4" hole drilled though the center, some could make a case that that is now a HSS and would need to be qualified via Clause 9. Unlikely, but possible.