It can't be too hard to make a plate that limits movement and can switch from 4 way to 8 way to open via an electrical motor.
I was thinking the same thing myself. As much as I like GGG"s OMNI-Stik, I don't like how that tiny tab sticks out. Plus I have to remember which direction is which and which games require which mode. If we had a motorized version, then it would become a software based solution automating the whole process. Add a color status light indicator, red for changing, blue for 8-way, green for 4-way (or whatever colors one chooses). Base the whole thing on 5v, use a LED board controller from either GGG or Ultimarc to control directionality. Or add a USB controller right on the joystick itself if we feel we need status feedback from the joystick (eg, whether it should be in 8-way mode, but it's stuck on 4-way mode). All the components are there, except for the joystick.
With an electrical motor, a whole new restrictor plate would be needed, likely involving worm gears to overcome the torque needed in a worst case scenario (someone holding the joystick on a diagonal during the change). Basically make the restrictor plate one big gear and place a worm gear on the motor. Maybe those 12v power window motors might be small enough and powerful enough to do the job? I'm not really an engineer type person so I'm sure there are much better solutions.
With a solenoid, you still have to overcome the torque limitations, but I think the restrictor plate can be made a little looser to allow adjustment. I think a solenoid design might be easier to construct using existing
switchable joysticks. One solenoid to do the switching and another to lock the plate into place.
I have a few more ideas, but they're a little bit more exotic.