One reason (at least) with two parts: US cars are too large, and fire departments in the US cover massive areas.
American care are huge, so fire services rely on their trucks to clear obstructions in an accident. In asia/europe, manual clearance is still the norm, but you just can’t do that with ex: a rolled F350 that’s blocking stretcher access down a two lane road. And given how remote a call might be, every second matters because its 25 minutes by air to the nearest hospital.
The other aspect is that huge coverage areas mean any given call could be in places of deep urbanization or the most remote rural bastions of podunkia. The trucks need to be able to go offroad, carry enough material to address emergencies entirely unsupported (big water tanks) and bash their way down a glorified ATV track. Dispatch areas are too large to have specialized FDs, so city roads have to be big enough to support trucks that can do both.
In short, we have to have big trucks because we won’t fund enough fire departments to allow them to specialize to a specific region’s geography.
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.