Funny, to me the physics of that floating backpack immediately check out on an intuitive level: the less energy I put into making the backpack move, the less energy I'll expend.

My only worry would be that it swings, and builds up more movement than necessary. In the video at 0:46 the movements look pretty excessive.

I imagine one could dampen the motion by regulating the tension of the bungees? or maybe lock it entirely if you need to jump around for a while?

I think that kind of shock absorption and momentum conservation optimization over something that happens tens of times per minute (like steps or strides when running) would definitely make a difference.

I'm poor at mechanics but afaik in racing it's considered that extra suspension absorbs energy, making the car slower. So my intuition is that the bungee cord would heat up from expanding/contracting, while taking energy for that from the person. Not sure, though, how that compares to lifting the entire weight. But then again, what happens when the person is already on a downswing and the cord belatedly jerks the backpack up?