Paul: "Slieve and Graeme reported (if I remember correctly) that with their SJR setup, there really only is the halyard and the sheet. Simplicity at its best."
Getting away from the thread topic a bit, but for the record, that is not quite correct. A feature of the SJR is that the batten parrels are running, not standing. The batten parrel lines are in spanned pairs to the deck, so on a Amiina rig you can manage with two lines which need to be adjusted along with any change to the halyard. If the batten parrel span itself is kept quite short, adjustment is not an urgent matter and just a tweak-till-firm is needed anyway, so not really an "adjustment". Still, we can not claim that only halyard and sheets are needed.
I believe Steve's Serenity with split rig and D-former rigid batten parrels needs only a halyard and a sheet. (Also, due to the rigid batten parrels, that sail is able to break the yard-angle/mast-balance "rule of thumb" and that enables an unconventional planform).
Paul's comment (absence of the usual running lines) relates to planform, of course - not directly to the split.
"So, when using high mast balance the call for huge rudders might fade away."
Not quite, in my opinion. I think a single mast junk rig with no headsail might always tend to be a bit hard-mouthed on a reach or run, depending a bit also on the hull shape, but I never had any doubts from the beginning that I would always want as high a balance as possible. I grew up as a kid learning to sail on an over-canvassed cat-rigged little boat that was very hard to handle off the wind, needed all the rudder you could give it, and the prejudice has never left me.
I always thought these down-wind antics were due to "all the sail area out one side" - but now we are using balanced rigs, Arne's take on it is: "the distance of the centre of area of the sail from the mast". I think it is to do with the distance between the centre of effort of the sail, and the centre of yaw of the hull - both rather elusive and variable critters. In practice, Arne's definition is good enough. So, a balanced lug should be easier on the helm than a conventional cat rig - and the more balance the better, from the helm point of view.
What little actual experience I have with junk rig is restricted to coastal only, and on a relatively small boat. Some of this discussion, however, amounts to little more than basic geometry.
(The downside of high mast-balance is that with conventional planforms, a taller mast is needed for a given area of sail. The helm issue (distance of CoA from mast) can also be addressed to a small extent by going for high aspect ratio of course. But there again there is a law of diminishing returns as this too requires a taller mast if you want the same amount of sail area).
Obviously sail design is a package - a judicious combination of solutions to many requirements - mast height, sail area, aerodynamic efficiency, ease of handling, simplicity of rigging, performance when reefed, behaviour in a seaway, proneness to "tangle-ups", simplicity of construction ... the deciding factor is not "this thing" or "that thing" - it's harmony.
And, last but not least, another matter of simple geometry - the placement of mast position in the boat (often dictated by bulkheads, structure, interior accommodation etc). On a single-mast rig, mast placement virtually determines the mast balance of the sail, and all that flows on from there.
Fortunately we have this range of possibilities which have all proven to be eminently workable.