Ok, I was referring to things like rock crawling and certain kinds of mixed or heavily rutted trails. You just don't do that sort of driving in the military, at least we never did. We air our tires down so that they can conform to a surface and in some cases the sidewall itself helps provide traction enough to help get you through.
The idea of anything like this surviving an IED, well someone got a general to give them some money, with a smile and a few good lines of BS. Let them make the tire survive, it won't matter, when you have an IED go off that close to your vehicle for the tire to be a concern, it removes the suspension and all.
They might do well at surviving weapons fire and shrapnel, so that's the best use case I can see for it. Current tires on combat vehicles already have a solid run flat piece inside the wheel. Unfortunately if you get your tire shot up sufficiently the tire starts to fall apart and really screw with the vehicles ability to drive along. It will still go but speed and maneuverability tends to matter too.