None of my grandma's were like that one in the picture, and they never caught fire, so I guess they were perfectly safe. But I'd assume they disappeared because they weren't UL compliant or some such. I honestly wondered how they could've been safe with that "plugless" channel they had for plugging stuff into.
Her house, built in 1950 only had 4 circuits total originally with a 60 amp service. I learned this when we re-did every inch of wiring in the place after a catastrophic flood in 2008. I did a full out autopsy on the electrical and to say it was interesting is an understatement. I learned an incredible amount about 1950s wiring techniques and about all the add-on jobs that came along after that. By the time we gutted the electrical the house had a total of 12 or 13 circuits, and a Federal Pacific sub panel for the 1960 Carrier furnace and some part of the basement. But anyway, the original 4 circuits were done much like the wiring in my dads 1915 apt building was, with 2 circuits staggered across the house. Then the other two circuits were; a dedicated 20 amp small appliance outlet in the kitchen, and one for the basement or furnace or something.
There were so many electrical additions done to that house between 1950 and 1975 that it was crazy IMO. Since it was built, central air had been added in the 60s, a room addition put on in 1960, the basement got finished and wired with outlets out the wazoo, the porch got enclosed into a year round sunroom. etc etc etc. By the early 70s somebody finally threw in the towel and upgraded the original fusebox to a Square D QO breaker panel, but never did bother to upgrade it from a 60 amp service. We wound up upgrading it to 100 amps in 2008. Of course all these additions to the wiring meant there were alot of unsafe modifications done, that is almost a story all in itself.
I could keep going on about her house, and not to mention the other places I've worked on but I think I'll save it for later.
There are two things I would never want to live with in an old building, one is electrical, and the other is those old brass gas connectors. Those two things absolutely terrify me. Like, so much that I wouldn't even move in until the electrical has been thoroughly inspected and all devices replaced/checked and the gas connectors replaced with stainless steel ones along with all piping checked out.