I told you it was a good question! It has got me diving through the library anyway. We know that early habaki were sometimes at least made of iron. We know that blades that have seen many polishes are unlikely to have the original habaki as the fit becomes worse as the polishing removes metal. (We also know that it is probably the most neglected of fittings as far as the literature goes, I would be very happy to be proved wrong on that). Most modern photographs are taken with the habaki removed for very good reasons.
The only reference I can find that specifically mentions the advent of the niju habaki is Stone who in his Glossary states that the niju form is the earlier but I am not sure how he arrives at this conclusion nor does he evidence it.
I have heard that the niju habaki is more common on lighter blades though this idea only makes sense when you are looking at a blade in koshirae, once the blade has been polished and put into shirasaya then the choice of habaki is essentially aesthetic. I am not sure that a niju habaki would be easier to fit to a sword with a thicker nakago due to polishing, the very fine one that I have on an Oiei Bizen wakizashi, clearly made when the sword was put into shirasaya, is interesting. The internal shape of the habaki has been made to fit the grooves that run the length of the nakago and the internal profile is consistent throughout the length of the habaki. When fitted the habaki has clear gaps between the faces and the surface of the blade but it fits like a glove elsewhere. As far as the fit to the blade is concerned then the register at the machi is the most critical I believe; once the nakago is seated in the tsuka and the mekugi inserted the fit in the tsuka and the slight pressure against the machi is what gives solidity to the whole thing.
To follow up on the point that Denis makes I wondered if saya shi would cut a shoulder for the larger part of the habaki. I have been looking carefully at the saya mouth on any of mine that have niju habaki and I cannot see a shoulder but in reality the shoulder is very slim in any case so given the soft nature of Honoki would soon disappear.
I can quite understand Mr Hagenbusch suggesting a single copper habaki suiting a sue koto katana, niju tend to be slimmer and perhaps not quite right on a sword with imposing sugata.
Not that this helps the discussion but I do have one sword which has a beautiful niju habaki that has then had a single silver foil jacket fitted covering the whole thing and effectively making it a hitoye habaki. The sword is in koshirae so probably the owners fancy.
Great fun but not sure that we have the answers yet.
All the best and thank you for making me look even harder at some of my swords.