What about printers without ink?

Laser printers have existed for a long time and they don't use ink, but they do use toner. I'm gonna assume just scorching the paper has been proven to be a bad idea, because someone would have tried to market a toner-free printer by now otherwise.

My best guess is that it's very hard to scorch paper to a color anywhere near black without creating a serious fire hazard. Even if you could calibrate the laser just right, the next batch of paper could burn because it has a slightly different weight, texture, or composition.

You'd probably end up being special paper stuff something in it that turns black at a fairly low temperature. That's pretty common for things like receipt printers.