Hello,
I was not sure if Kurt is your first name or last name so please excuse the informal greeting.
In my opinion the 'why' for a sailing rig is almost entirely personal preference. This may be even more true for rigs that are an 'alternative' to the Bermudian rig on the majority of production boats.
Below are a few reasons why I, personally, prefer to have one sail, not one junk sail and one headsail.
1. Minimizing running rigging. I have four running lines, including the sheet. This lets me do all the normal sail handing, including reefing.
2. A stayed rig has dozens or hundreds of small pieces that all must hold to avoid dismasting. An unstayed rig only has one big structural spar.
3. A single junk sail is self tacking. It is possible to make a headsail self taking as well, but this is not common.
4. Only one sheet to trim for all points of sail.
5. No flogging dacron when tacking or easing the sheet for any reason. A single junk sail is very quiet in most any conditions.
6. A jammed roller on the headstay in a strong wind seems absolutely terrifying.
7. No need to use 'real' dacron sailcloth at all. The Weathermax LT I used is much easier to handle and sew than fresh stiff dacron.
8. Side stays will always cause some interference when easing the main sail out all the way. I like the ability to sail by the lee on a beam reach. It feels like magic to sail on the same tack close hulled, then a beam reach, then a run and then to a beam reach on the other side of the hull by adjusting only the sheet.
9. It is much easier to step and unstep the mast with no shrouds or stays to get tangled.
10. I am able reef without pointing the bow directly into the wind. In fact, most of the time I can drop the first two or three panels while running dead straight down wind. From what I understand this is not feasible with a roller furling jib.
Scott.
edit: four including the sheet.
edit2: added #10