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"
Also, in my town, the firefighters are also paramedics. The first people who showed up in my Moment of Need came in a fire truck. The ambulance came a couple minutes later.
The hospital facilities team removed the front doors and the unboltable parts of the frame, and then gassed off the handrails and wheelchair ramp fittings to give access.
The ambulance arrived followed by a fire brigade Landrover with four guys in and a rescue pump with another five. It took all of them to lift the patient into the hospital on a canvas sling.
Anyway I’m not against paramedics wearing boots in my apartment, in an emergency very few people would care about that even in Japan.