Here in America, EMS personnel generally wear tall, reinforced boots; they are considered protective/safety equipment. We would never take them off just to enter a home
Throughout my fire and EMS training I was taught to anticipate possible violence from the residents. I personally know folks who have entered buildings and been shot at or found booby traps. One guy I know responded to an arson house fire where the resident had cut out holes in the floor under every window and door and covered the holes with rugs, Home Alone style.
The US has a serious drug and mental health crisis. First responders often have to deal with people who probably would be in state care if we didn't spend all our tax money on bombs and tax cuts for the wealthy. Or at least they would have caretakers who visit and help them take medications and escalate when they start setting up booby traps to defend against the voices.
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"
Anyway I’m not against paramedics wearing boots in my apartment, in an emergency very few people would care about that even in Japan.
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.