There is no way you are getting a massive fire truck offroading or down an atv trail. It wouldn’t have the traction or turning radius for much off roading outside of a farmers field. Smaller, lighter fire trucks equiped with all wheel drive systems would be far more effective. They could also be equiped with winches to move all those f350s that rolled over.
You’re in emergency services, I take it? I’d be shocked if at least one of your engines doesn’t have a winch on it. Our local dept. uses theirs all the time - after Narcan and the bolt cutters, it’s probably the most used tool on our trucks.
Engines can, and absolutely do, travel off road. Look at news coverage of any wildfire for examples. Are they 4x4 offroading or ATV tracks? No, I was quite clearly being hyperbolic, as indicated by my use of “glorified” as a qualifier. But you would be amazed at what kind of off-lot mudding backroads you can get an engine down when you need to.