Everyone except the driver has ample time to swap boots during the drive to the location. (In cases where not, I'd also default to robust safety boots.)
Depending on the boots, you might not want to wear them while "idle"¹ in any case, though that's mostly a non-concern with modern safety shoes.
¹ mandatory note: most emergency responders have tons of work while "idle", I just mean "not actively responding"
You don't always know what the location is like though. You are called to an apartment: maybe it is spotlessly clean, maybe the floor is littered with used needles