And then there is stronger braking to be considered, which almost always is some kind of disk brake which you can't do if there is no shaft to mount one on. Which means the spherical wheel system would have to be oversized to compensate for lack of such a shaft even if it would work to drive the car. Magnetic wheels have other interesting problems that would need to be solved such as when two cars get close to each other the wheels would start to attract or repulse depending on their orientation.

This is mostly likely not something that could be rolled out even in a concept car with present day technology unless there is some kind of trick that I'm not aware of. Halbach arrays are not without problems if you allow them to be unconstrained in all dimensions.

If they are too big then the car will only have room for two: one in the front and one in the back.

TaDa: the self driving Tron motorcycle!

Could you just use standard wheels, but let all four of them turn 90 degrees? Then the car could move laterally.

There are some cars that already do this.

It's a lot simpler with independent electric motors per wheel, but generally not that useful as self drivings cars can already parallel park just fine.

You only need one wheel to turn very tightly:

https://www.youtube.com/watch?v=YlLZE23EJKs

That's true. But then again, I did come up with live streaming video on the web and some other lesser known bits and pieces of technology. And I'd argue my lego sorting machine also required plenty of creative thinking.

There are definitely major challenges, although maybe those could work in areas where the motion is slow but constrained (e.g., a cart to move cars in/out/around a dedicated parking lot). Maybe flatten the surface used for normal motion and use sides for infrequent, slow maneuvers. I do not know.

But those ideas are tangential (being generous) to self-driving, so better not steal cycles from it.

Plus the whole sphere and its housing is going to take up a lot of volume.