I think we can roughly split paramedic visits into “patient needs to get out ASAP” and patient can’t get out alone or with help of friends and family”, so I would hope they keep their shoes on for the first type.

But ambulances in with full sirens begging over their speaker-system to have pedestrians at Shibuya crossing let the vehicle through, is probably the worst thing about Japan.

As for your second question, I’m reminded of Bob Mortimer in Would I lie To You: “… then the fire brigade came and ruined the whole house” - “Bob, surely the fire was ruining the house” - “No, water damage”. Maybe if those darn firefighters had taken their boots off, there had been a bit more left of Bobs childhood home.