I think it's difficult to generalize across the entire IF range of bikes. While they all employ similar technology it seems that the devil is in the details.

In the case of the IF Reach and IF Cross I would agree that the swivelhead feature does not, in itself, provide much benefit. There are, however, other features of the IF design which seem to offer clearly superior ergonomics to Dahon, namely:
1. The right fold separates much of the drivetrain from the outside world, offering both protection of the
drivetrain against bangs and protection of the outside world from grime.
2. Related to #1, the wider separation of the wheels provides a more stable base on which to stand/roll the bike, a feature which appears to be further enhanced by toe in of the side-by-side wheels.
3. The main hinge appears to be designed to use as a handle for pushing the folded bike along.

While these features could all easily be incorporated into a Dahon-style fold without a swiveling headset, I think the important point here is that so far Dahon has been unwilling to consider such ergonomics in their designs. As jur said, whereas the folded ergonomics of a Dahon bike is entirely accidental, the ergonomics of the IF range are specifically designed. Dahon could make their bikes fold to the right, but they don't; Dahon could make the wheels of their folded bikes toe in for rolling stability, but they don't; and Dahon could make the most natural grabbing point (the main hinge) for rolling their bikes shaped like a handle, but they don't. To me the biggest selling point of the IF Reach and IF Cross is simply Dahon's unwillingness to pay attention to the details. While the swivelhead probably does also shave off a few inches of protrusions, it is a minor benefit compared to the overall attention to detail (in my estimation).

The IF Mode, on the other hand, seems to be an entirely different beast which puts the swiveling headset to maximal use without compromise. The clear advantage of this bike is that on the folded bike the headset lies completely parallel to the main frame, completely eliminating the protruding headset/handlebars found on almost all folding bikes (including Dahon). With this cornerstone in place, achieving maximal compactness is simply a matter of correctly shaping the frame to fill the gaps in the folded package and eliminating wide parts like derailleurs and double sided axles. The end result is a bike with full size wheels whose folded volume is as small as a Brompton. In the case of the IF Mode, how could you question what it has to offer over a Dahon? What full size Dahon even comes close to twice the folded volume of a Brompton?