I don't think the requirement for printed output requires any appeal to military applications. They would have been exchanging navigation information with mission control over the radio. That's all mission critical and needs to be read back. Anything they got via voice they would have to write down. Getting it by text in the first place would increase reliability and reduce cockpit workload.

You also get in-flight information like weather that you'll want to write down for later reference. Teleprinter writes it for you so you can review it at your leisure.

Airliners and ships at sea have both historically used teleprinters for the same reasons, although the modern navigation computers have mostly eliminated the need.

Oh, I didn't consider that, since I was a young person then. Sticking notes, directives, etc, everywhere was just really common. So if they get a note about extra daily checks on equipment X, they print/affix the note to the equipment. Or other similar needs. There would probably be limited screens, so anything you wanted to be known to everyone, becomes a note.