I remember when I was at school about 15 years ago there were printers that used wax(?) blocks, that were just put into it, not sure how it worked exactly.
Advantages: waterproof print; very clean; easy to change ink blocks; maintenance was mainly just emptying a tray containing small amounts of waste wax (biodegradable)
Disadvantages: when offline, the printer still used power to keep the wax in a liquid state, otherwise a cold start could take a while; colors were occasionally not as vibrant as regular laser printers
We had a tektronix with blocks - and that one had to be kept off except for very specific times, because if left on it would stay warm and over a week or two drain all the wax out of it into the waste tank.
Tektronix did a range of printers that used wax. They used rolls of wax sheet. They produced fantastic output, but the rolls of wax were really expensive. And if you put a coffee mug down on a printout, they got stuck together.
I think they were meant for one-off proofs of image-heavy marketing material. The colours were intense and vibrant, in a way that no colour laser or ink-jet ever is. Also, the wax stood a bit proud of the paper, giving an embossed look. But they weren't very permanent - if you folded the printout you'd damage the image; you could even scratch the wax off with a fingernail.
Advantages: waterproof print; very clean; easy to change ink blocks; maintenance was mainly just emptying a tray containing small amounts of waste wax (biodegradable)
Disadvantages: when offline, the printer still used power to keep the wax in a liquid state, otherwise a cold start could take a while; colors were occasionally not as vibrant as regular laser printers