I see the beauty of such out-of-the box thinking. It's a very fascinating consept. I think many systems should be built with less rigidity, so they could withstand more extreme conditions without collapsing. Doesn't this actually resemble a human body where bones take mostly one-dimensional pressure, while muscles and tendons determine position and shape. It's never completely rigid, but is extremely energy-efficient, and can take all kinds of different loads and impacts without collapsing.

Could tensegrity structures be thought of as systems with negative feedback loops, which always attempt to return the system to it's natural state? A house of cards would have a positive feedback loop: you take away one card, and the feedback loop destroys the whole house.

Usually you would want a rigid structure. Those too can be built to withstand abnormal circumstances. Think of antic Roman stone structures, that have stood for thousands of years, with earthquakes, floods, storms etc. It's more comfortable to stand on something that doesn't wobble, as long as it doesn't collapse without warning :-)