>The solution is to mount the entire assembly on a spring/strut & damper assembly.
Spherical Wheels. "Squishy" tires must be used to maintain road traction but, how to mount them to a rim? Without a rim a semi-ridged tire would have to be too stiff to absorb road shocks or if soft enough to absorb micro moments and inertia changes it will deform too much and cause overloading of the wheel support rollers (bearings) This will lead to a problem with friction/ware,, Not having a conventional cone/cup bearing the shock moments will not pass thru to the shock absorbers easily but will spike in the wheel support socket and will cause un-wanted drag and ware on the tires. balancing the wheel is another problem altogether. Tread design is also a problem. the tire must have some type of tread design to reduce the chance of a hydroplane. But how to orient the tread pattern when the omni-directional nature of a Spherical Wheel will change with every turn or change of direction. tread design may not be so much of a problem but the grooves will carry dirt and road crud up into the wheel socket. Now should we discuss brakes? Magnets under the rubber tire and windings in the socket to make an electro magnetic brake would be the only way to prevent excessive ware on the tires from friction. But this goes back to how to mount the tire on a round rim.
Most all of these problems may be over come with a magnetic levitation / propulsion / braking design.
Good point...
Mounting the tire to a rim would not be difficult... There are currently available foams which take the place of pressurized air inside a tire, thus allowing the manufacture of tires which are "married" to the rims... This would be expensive, but definitely do-able.
The issue would come with the warping of the flexible tire, which could cause lock-ups, if it compressed too much. I suppose the only real solution to that issue would be to find the right balance of "squshiness" and rigidity, while keeping the housing at just the right size to prevent lock-ups from a compressed tire, while still holding the spherical wheel in place. I don't know that this proper balance could be found, but it seems to me like such is possible...
Tread wouldn't be too much of an issue, provided the power wheel was encased to prevent dirt and debris from jamming up it's workings... Same with the brakes, which would be a bit trickier. (Come to think of it, there would be an issue with the braking system I described, if the tires were too soft. But once again, the trick is in finding the right balance.) The tread pattern could be a simple diamond pattern, similar to that on tractor tires, but symmetrical (as opposed to the elongated tread of tractor tires.)
It seems to me like the shock absorption system of the entire wheel assembly would account for much of the bumpiness of the ride, which in turn would make finding the balance between soft & rigid tires possible, but I haven't done enough math to know for sure. I'll be doing some work on the design tonight, so I should have some drawings and math to post tomorrow, if all goes well.
I'm not convinced that it's possible. I AM convinced that it's worth looking into.
Keep thinking of problems, please

It makes my job so much easier, not having to figure them out or discover them unexpectedly myself