Unrelated to the new movie, but I just read how blade runners came to be called blade runners. It makes even less sense than you thought.
My summary won’t do the story justice, but essentially an unknown doctor wrote a dystopian novel in 1974 called The Bladerunner about a future where people had to be sterilized to receive medical care. A black market of doctors and clinics was created, and “bladerunners” were the people who secretly supplied the clinics with medical gear such as scalpels. William S. Burroughs liked the book and licensed the rights for a movie. But he then wrote a bizarre screenplay/novella that had little to do with the original book and, being written by Burroughs, the movie was unfilmable. So instead he published it as a book called Blade Runner: The Movie.
In the early 80s when Ridley Scott was working on the adaptation of Philip K. Dick’s book with the producer and writer Hampton Fancher, Scott asked what they should call the detectives. Fancher happened to have the Burroughs novella on his shelf, saw the name and thought it sounded cool.