Why were there pneumatic headphones on airliners in the 70's and 80's?
Well, the rubber hoses themselves were used instead of traditional electromag transducer headphones for two main reasons; first, the hoses were much cheaper than a decent pair of traditional headphones at the time, and to an extent they're washable, so airlines could provide a pair for everyone at a much lower pricepoint than traditional headphones. Second, the hoses were more or less useless without the driving system aboard the aircraft, largely removing the incentive for passengers to walk off with them, again reducing costs of providing the system to passengers. The system was phased out in favor of simple 1/8" stereo jacks at each seat in the '80s and '90s as portable audio became mainstream, and as airlines looked to dramatically slash costs in the face of deregulation beginning in 1978. Economies of scale meant that buying cheapo Walkman-style headphones in bulk became cheaper than maintaining the aging pneumatic systems, and the electric-based system was more reliable and had several advantages (such as volume control for each passenger, and if standard 1/8" jacks were used, the ability for a savvy flyer to bring their own, nicer pair for use on the flight).

As an aside, this pneumatic audio system is still used today for a very different purpose; newborn hearing screenings. A pair of flaps with a mild adhesive are stuck to baby's ears, then hoses lead back to a finely-calibrated audio system coupled to an EEG. Audio is played and the EEG is monitored to detect the response to the sound in baby's brain. The hose system is used because it allows the expensive, fine-tolerance part of the audio system to be reused from test to test, while the hoses themselves are disposable and (as hospital equipment goes) fairly inexpensive.