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
Probably the same in most Western countries. It's self reinforcing though; if you were expecting to take them off you'd never pick those shoes by default, rather leave them in the back of the car (which presumably/hopefully is what they do in Japan, in case they *do* need them? idk…)
It also seems quite dangerous to take them off- depending on the home. Some hoarders, drug addicted situations have needles, glass shards and razor blades in the debris on the floor. How do they handle hoarders in japan?