Thanks gents, for those clarifications. From what
@tkarhu and
@DG99 have said, and the diagrams and video, it looks like there are a wide variety of configurations. For the Voile Switchback ("Yeah, I've been ready for a while actually"
) it looks to me like when the toe plate is in pivot mode, all the spring/cable is doing is keeping the boot in the binding unless you manually force your toe onto the ski. Only when you lock the toe plate down do the springs start imparting moment to the ski. Interesting. Is this primarily a way to simplify the transition from kicking to skiing? All you need is a pole!
For
@tkarhu 's Swedish Army Binding, it looks like the cable both retains the boot in the binding and provides some moment. My guess is that this would be a very simple system suited to the needs of ski troops as opposed to recreation which would likely want to be useful over a wider range of conditions.
I find myself wanting to make a simplified dynamics model of these systems and run it in Matlab/Simulink. (The first thing I'd neglect is sole bending other than at the toe. Too hard to model!) I think I'd find that the more recent toe-only force systems require more control authority and display greater sensitivity to input uncertainty and perturbations than a cable-spring system. (I.e., they are harder to learn, harder to control, and have a smaller envelope.) I don't know that I'll actually do this since I'd really rather be out skiing and I do similar things at work. And it wouldn't be helpful in design or sizing since the model would be too simplified to be used for generating any kind of specification. All it would do is verify what users have already reported.
Oh, it would also let me vary the configuration and put a stake through the heart of the physics debate!
Maybe worth it after all???
But it does leave me wanting to cobble together an Xplore/Cable frankenbinding and test it out for grins. There are a bunch of used cable setups available locally in the $150 range. From all I've heard I think I'd probably really like a 75mm cable system but I've played the find-used-boots game with motorcycles and it's just not fun for me anymore.
Incidentally, my wife views this level of interest in something like this as some kind of insanity and I'm going to take a wild guess that I'm not alone, here. Then again, warm houses during the winter, automobiles, and many other modern conveniences are due to this primarily, but not exclusively, male fixation on how things work. I hope that makes me a sexist. I try to check at least one box a day.
Swedish army skis are Wooden planks with zero sidecut. 
