What I see is that If you draw the ring profile as periodic curve, that curve will be natively SubD Friendly.
Then you have a chance to not face the described behaviour when using Sweep 1 ( Right on the picture )
Ring profiles; depending on the drawing strategy applied, are often composed of a set of curves of varying degree ( left on the picture - 2 lines of D1 + 2 curves of D2 or 3 )
Converting these curves without impacting the shape sometimes leads to a compromise.
In my humble opinion, in some situations, I find more relevant to draw a ring profile in a specific way that better correspond to the needs instead of trying to convert an object to match the needs.
…which often leads to unwanted complexities or extra modelling steps.
I think it would be useful to have an option allowing to better manage the resulting curve structure while running the command MakeSubDFriendly.
Hope it helps.