My mom slept in one of those once, on a transatlantic flight. Must have been around that time, now that I think of it. Thanks for the ads!
If you can swing biz class on one of the fancy Middle Eastern lines (Qatar Air) or upper class on Virgin Atlantic, this sort of thing still exists. I worked for a while overseas and was able to fly this way and I cannot lie, IT IS AMAZING. VA has these cute diagonal seat pods that fold out and they bring you a down comforter. QA's super fancy first has ACTUAL ROOMS. To say I was disappointed when the company elected to fly us coach the last year I went is an understatement.

Also: VA! Has airport lounges! With free, AMAZING food! LIke, RIGHT THERE at the airport, and it's full of people acting like this sort of thing is TOTALLY NORMAL. My mind was blown.
Yeah, but back then you probably wouldn't have been able to afford it. That $55 up-charge for a berth in 1956 is equivalent to $450 today -- for an up-charge, not for the base ticket!
I would've liked one when I flew to Hawaii, even though my flight only lasted seven or eight hours.
Y'know, it occurs to me that these long-haul sleeper services would have been hell on the crew. And the thought of being trapped OVERNIGHT in a plane with a screaming kid makes me shudder.

That being said it still looks like a lovely way to travel!
I neeeed one of those. Especially if I'm going to visit my mother in California. Eighteen hours!