Ditto jerryjanis, but some more info:
There are 12 position player games (example: caliber 50), but they usually used optical rotary joysticks (list of most rotary joystick games
controls.dat).
Also, the forgotten worlds I first played had a spinner that could be pressed to fire & a normal 8-way joystick. Later forgotten world cabs I played had optical rotary joystick and a normal button. The op manuals say the former is the offical way; I guess the latter is an upgrade kit or hack conversion.
FWIW, I like being able to shot "360" without having to spin the joystick 360. Try taking your hand like it's holding a rotary stick turned all the way one direction, and see how far your wrist can turn all the way to the other direction. My thumb goes from the one o'clock (or 1:30) position backwards to the 4:30 position, about 8 hours (or positions) in a 12 hour clock. A smart design, IMO.