My Donkee is about 10 years old. It does wobble a little on the low setting, but not enough to pose a problem. I have mine on a rubber mat to dampen it a bit. Even though others have done so without any issues, I'd hesitate to bolt it down. If you don't give the vibration somewhere to go/release, I'd think it would place a lot of torque on the shaft and housing.
I rarely use the high speed, but if you only use it for cleaning and polishing there isn't a problem. Just place the ball in the most stable position for the core and you won't have any problems. A highly asymmetric ball might wobble more, but for me they are usually my oil balls so I never apply polish to them. If you need to sand 4 or 6 sides I only ever use the low setting. When the core gets too far off center, it can wobble a lot on the high setting. In my opinion, you don't need the high setting for sanding.
For home use with a normal arsenal, I think the Donkee is perfectly acceptable. If you are trying to maintain equipment for several other people, you might look at other options.