I've heared of quite a few people who have that mind set about applainces, but honestly, the worst that happend to me in that fieled was a sheet of backing paper igniting because it touched the ovens broil element.
While I get the idea, I just always remember myself that microwave, oven, fridge, freezer and our WiFi-router are all still plugged in an pose a simmilar hazzard of fire as my alarm clock does: Barely any.
I think the only applainces that I would never have running without me around would be the oven and hoob, simply because even if you attend them, a lot can go wrong.
In terms of floods due to defect machines I guess I understand why everybody is so carefull there, water is awesome at ruining living spaces.
In Germany, however, if I got that right, every property that is rented out has to be insured against flooding damage. These policies require the use of those burst-safe hoses and that instalations are done by professionals.
But I trust my aplainces there that they don't destroy my flat... Maybe a bit much...