This is just a data point, not a definitive answer, but I think my “I have not seen one in a long time” answer is pretty much OK, as I do travel a lot.
I would also suggest you go to a more authoritative source, www.flyertalk.com, and post your question there. For frequent flying/air travel/ they are kinda like the SDMB. Warning, there is a lot more “noise” there, but there are some real gurus who could give you a better answer, I think.
They still have them, but they are not as common as they were in years past. I have seen them in LAX, Burbank, Seattle and probably Reno but it was hard to see around the slot machines.
With the incredible run of flight safety in the past 7 years, that is one business I would like to run. Those have to be some of the most profitable insurance policies around.
So how did those work? Did the vending machine dispense a multi-part form along with an envelope to send off part of it to a trusted party such as your spouse before the flight?
I can’t imagine it would do any good if you took the whole thing with you on the plane.
I believe the machines provided a form and postage paid envelope so you could mail it to someone. This is based on a vague recollection of getting one from my wife when she flew by herself, before I told her not to waste money on it.
Back in the day when they were common, I would occasionally give someone flying a couple of dollars and ask them to get some flight insurance and put me down as beneficiary. I’d say “I don’t know, I just feel lucky.”
It was a postage paid envelope, and I think there was a depository right next to the machine, IIRC. I think I did one once as a kid for fun. There were a lot of pages, and back then I thought that was cool.
I remember them being in the lobbies back before security. Are the ones in LA, etc. by the gates or before check-in?
I haven’t seen one in ages either. I seem to have read about how credit cards now often give insurance if a flight is bought on the card, so many people have insurance already. Also, back 40 years ago there were a lot more first time fliers, and flying was a bit exotic, so no doubt there was a bit more fear.
Lenny Bruce has a bit, called Non-Sked Airlines, based off a supposedly true story of a guy who bought insurance for his mother and sent her off on a flight with a bomb.