I'm modern enough to have rotary control on the amplifier. But that rotary control basically gives identical use as a potentiometer, which is the reason I didn't count it as a third alternative. The rotary encoder is basically a digital potentiometer. The only real differences are:
- volume changed in dB steps instead of continuusly.
- no end stops, so I can spin it for many turns (which obviously doesn't change the volume after max or min volume has been reached)

Many potentiometers have mechanical or optical encoders instead of potentiometers, to give better linearity and having them survive many more cycles - and potentially deliver a digital instead of analog output signal. But there is a huge difference with a joystick compared to a rotating knob - a joystick can't support infinite turning angles (and our hands wouldn't be able to work well with such an imaginary joystick either).

The only ways you can get a joystick to produce intuitive results is if you:
- normal proportional use. when centered, the controlled device returns to idle position or idle speed.
- digital on/off controller where activation of joystick gives constant acceleration or movement speed (with optional acceleration depending on activation time) and where a release of the joystick means the acceleration (not speed) of controlled device returns to zero.
- analog controller where the twist angle controls either position or acceleration of device.
- have a joystick that does not self-center, so it (like a normal potentiometer) keeps the current setting when released.

But use of a joystick with a "set" button leads to big problems.
- If you let that "set" button change the joystick offset, then the user may have a motor at 100% speed but a centered joystick. Not intuitive to figure out that pushing the joystick forward will not make a difference.
- If you don't change the joystick offset with a "set" button, then you will get a big jerk when the user tries to take control of the device again, because the user can't guess what angle to hold the stick to match the speed/position the device us currently having.