In the 1960s, I remember seeing DeskFax machines used by amateur radio operators.
Speaking of wet paper, in the 1970s (and perhaps 1980s), I serviced weather fax machines made by Alden and used at FAA Flight Service Stations. They used soggy paper that turned brown when current was passed through it. The machines had a drum with a helix on it. This rotated behind the paper to give the horizontal scan. A contact band was above the paper to provide the other contact. A synchronous motor fed the paper out of the machine to provide vertical scan.
Video was transmitted as analog FM on the telephone line with one frequency representing black and another representing white. Horizontal sync consisted of several lines of black with a pulse of white. This was run at the beginning of each image. There was a magnetic reed switch that detected the position of the helix drum. Both motors were run from a divided down crystal oscillator. During sync, the oscillator divisor was changed so ther motor ran a little slow. When the white pulse lined up with the reed switch closing (left edge of image), the divisor would be changed back to normal (which, I think, gave 60 Hz to drive the motor). This resulted in a diagonal streak of white in a black bar at the top of each image as the machine set synced up.
The top contact band also rotated (like a very slow band saw) to even out the wear on it.
The main problem with the machines was the power amplifiers that drove the motors. Now and then they'd just blow up. We'd call Alden and they'd send out a new set of boards. The machines were otherwise pretty reliable. We'd visit them monthly to clean them out and replace worn bands or helix contacts. That's about it. The FAA guys would stick these maps up on a bulletin board for pilots that came into the FSS to look at.
Other interesting stuff at the FSS was the way they reported weather. They had a paper tape punch. They'd make their weather observations, punch a tape, then put the tape in a reader. A while later the reader was polled by a central controller and the data was transmitted.
Speaking of fax, though, remember the original office fax machines that transmitted a page in seven minutes? For a long time (maybe even now) fax machines continued to have the seven minute mode for compatibility with the installed machines. I think those machines also used linear FM with no compression.
Harold