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…)
if you do need them you're not going to have time to go get them as an Emergency Responder. I think the pragmatic course then is to disregard etiquette and tradition for safety and practicality in a general sense.