The only time I have seen machine inserted wire links is in copiers and printers, where they will do wire links, either to use a single sided SRBP board ( cheap and can be made either additively using a screen printing process, or which can be etched fast) and up to 300 wire links, or on a double sided board so as to avoid having to use a multilayer board, but still having a ground plane on the board for EMI reduction. There they also often did the board as double sided but without through hole plating, using the component leads and links as connections to the top side traces. Top side was hand soldered as well with the bottom being wave soldered.
Saw a Sharp copier board with literally a single mask MCU, a decoupling capacitor, a crystal and 2 capacitors and a quartet of components for reset, and 300 wire links in neat rows across the board, in 2 orientations and 4 different lengths. All this and around 11 multipin connectors to the rest of the machine. You might have up to 10 wire links on a single trace, from one connector and going to another. All this to use a single sided board. It must have been cheaper than going double sided through hole plated by at least a few cents.