I think the inspiration may have been games like Cyber Sled or Battlezone, which in the arcades used a two-stick setup.
Indeed, the Playstation early in its life had a twin-stick peripheral.
The same Playstation also had the Namco neGcon, a controller meant for racing games, which used analog both for turning the car but also for gas and brakes.
As such, early on it doesn't take much of an intuitive leap to see why a general-purpose controller should have more than one analog stick, if there were already controllers that were trying to fake it.