Apparently basses specifically benefit from the headless setup for better weight balance, and iirc got that treatment first.

Edit: here it is:

Furniture maker Ned Steinberger is often credited with pioneering headless designs in the early 1980s. Having already collaborated with Stuart Spector on the NS-2 bass guitar, Steinberger felt further improvements could be made. To address the common issue of “neck dive”—the tendency of bass guitars to tip forward due to their long, heavy necks—Steinberger decided on a novel solution: to move the tuners to the bridge and omit the headstock entirely.